## Burrage, Kevin

Compute Distance To:
 Author ID: burrage.kevin Published as: Burrage, Kevin; Burrage, K. Homepage: https://staff.qut.edu.au/staff/kevin.burrage External Links: MGP · ORCID · Google Scholar · dblp
 Documents Indexed: 184 Publications since 1978, including 1 Book 3 Contributions as Editor Reviewing Activity: 270 Reviews Co-Authors: 135 Co-Authors with 162 Joint Publications 2,688 Co-Co-Authors
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### Co-Authors

 24 single-authored 27 Liu, Fawang 22 Burrage, Pamela M. 21 Turner, Ian William 15 Tian, Tianhai 9 MacNamara, Shev F. 9 Sidje, Roger B. 7 Jackiewicz, Zdzislaw 7 Komori, Yoshio 6 Zeng, Fanhai 5 Anh, Vo V. 5 Chipman, F. H. 5 Pohl, Bert 4 Erhel, Jocelyne 4 Lesmono, Dharma 4 Niu, Yuanling 4 Sharp, Philip W. 4 Welfert, Bruno D. 4 Williams, Alan B. 4 Yu, Qiang 4 Zhuang, Pinghui 3 Alcock, Jamie 3 Belward, John Alan 3 Bueno-Orovio, Alfonso 3 Butcher, John C. 3 Chen, Changming 3 Lythe, Grant 3 Suhartanto, Heru 3 Tonkes, E. J. 2 Altas, Irfan 2 Brugnano, Luigi 2 Carletti, Margherita 2 Chen, Jinghua 2 Chen, Luonan 2 Cusimano, Nicole 2 Dayan, Peter 2 Donovan, Diane M. 2 Goodhill, Geoffrey J. 2 Herdiana, R. 2 Hundsdorfer, Willem H. 2 Karniadakis, George Em 2 Kerr, Minnie 2 Lawson, Brodie A. J. 2 Mac, Shev 2 Mortimer, Duncan 2 Piskarëv, S. I. 2 Renaut, Rosemary Anne 2 Simpson, Matthew J. 2 Somathilake, Lekam Watte 2 Walmsley, John L. 2 Weber Dos Santos, Rodrigo 2 Yang, Qianqian 2 Yazıcı, Emine Şule 2 Zhang, Chengjian 1 Abdullah, Farah Aini 1 Ahn, Vo 1 Baker, Christopher Thomas Hale 1 Berg, Lucas A. 1 Browning, Alexander P. 1 Cameron, Ian T. 1 Cardone, Angelamaria 1 Carreras, Giulia 1 Cavenagh, Nicholas J. 1 Chan, Robert Peng Kong 1 Chen, Phoebe 1 Chen, Shiping 1 Christen, Peter 1 D’Ambrosio, Raffaele 1 Dangerfield, Ciara E. 1 Ding, Xiaohua 1 Duc, K. Dao 1 Dyke, Carolyn 1 Eldershaw, Craig 1 Eremin, Alexey S. 1 Estivill-Castro, Vladimir 1 Farquhar, Megan E. 1 Fellows, Michael Ralph 1 Feng, Libo 1 Fine, J. M. 1 Guo, Ling 1 Hale, Nicholas 1 Hamilton, Nicholas A. 1 Hanan, James 1 Hegland, Markus 1 Hertono, G. 1 Holcman, David 1 Jiang, Xiaoyun 1 Langston, Michael A. 1 Leier, André 1 Lenane, Ian 1 Li, Changpin 1 Liu, Qingxia 1 Mapder, Tarunendu 1 Marquez-Lago, Tatiana T. 1 Mayer, D. G. 1 McCourt, Thomas A. 1 McLean, William 1 Mirams, Gary R. 1 Mitsui, Taketomo 1 Moroney, Timothy J. 1 Moss, Pamela ...and 35 more Co-Authors
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### Serials

 17 Journal of Computational and Applied Mathematics 13 BIT 13 Applied Numerical Mathematics 13 The ANZIAM Journal 12 SIAM Journal on Numerical Analysis 9 SIAM Journal on Scientific Computing 7 Computers & Mathematics with Applications 6 Numerical Algorithms 6 BIT. Nordisk Tidskrift for Informationsbehandling 6 Journal of Theoretical Biology 5 IMA Journal of Numerical Analysis 5 Journal of Computational Physics 5 Applied Mathematics and Computation 5 Advances in Computational Mathematics 4 Applied Mathematical Modelling 3 Annals of Numerical Mathematics 2 IMA Journal of Applied Mathematics 2 The Australian Mathematical Society Gazette 2 Physica D 2 SIAM Journal on Matrix Analysis and Applications 2 Communications in Nonlinear Science and Numerical Simulation 2 Multiscale Modeling & Simulation 1 Bulletin of the Australian Mathematical Society 1 Computer Physics Communications 1 Discrete Mathematics 1 Journal of Mathematical Analysis and Applications 1 Journal of Mathematical Biology 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Bulletin of Mathematical Biology 1 Computing 1 The Fibonacci Quarterly 1 Mathematics and Computers in Simulation 1 Numerical Functional Analysis and Optimization 1 Journal of Computational Mathematics 1 Parallel Computing 1 Numerical Methods for Partial Differential Equations 1 Journal of Scientific Computing 1 Annals of Operations Research 1 Neural Computation 1 European Journal of Operational Research 1 Linear Algebra and its Applications 1 Computational Statistics and Data Analysis 1 New Zealand Journal of Mathematics 1 Numerical Linear Algebra with Applications 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Journal of Applied Mathematics and Computing 1 Computational Biology and Chemistry 1 Journal of the Indonesian Mathematical Society 1 Mediterranean Journal of Mathematics 1 JNAIAM. Journal of Numerical Analysis, Industrial and Applied Mathematics 1 Journal of Fractional Calculus and Applications 1 Axioms 1 Stochastic and Partial Differential Equations. Analysis and Computations 1 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Cogent Mathematics & Statistics
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### Fields

 145 Numerical analysis (65-XX) 65 Ordinary differential equations (34-XX) 51 Probability theory and stochastic processes (60-XX) 35 Partial differential equations (35-XX) 33 Biology and other natural sciences (92-XX) 11 Real functions (26-XX) 8 Fluid mechanics (76-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Statistics (62-XX) 4 Computer science (68-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 General and overarching topics; collections (00-XX) 3 Integral equations (45-XX) 3 Operations research, mathematical programming (90-XX) 2 History and biography (01-XX) 2 Special functions (33-XX) 2 Operator theory (47-XX) 2 Mechanics of deformable solids (74-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Systems theory; control (93-XX) 1 Combinatorics (05-XX) 1 Number theory (11-XX) 1 Approximations and expansions (41-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Mechanics of particles and systems (70-XX) 1 Optics, electromagnetic theory (78-XX) 1 Geophysics (86-XX) 1 Information and communication theory, circuits (94-XX)

### Citations contained in zbMATH Open

157 Publications have been cited 3,718 times in 2,422 Documents Cited by Year
Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation. Zbl 1193.76093
Liu, Fawang; Zhuang, P.; Anh, V.; Turner, I.; Burrage, K.
2007
A Crank-Nicolson ADI spectral method for a two-dimensional Riesz space fractional nonlinear reaction-diffusion equation. Zbl 1382.65349
Zeng, Fanhai; Liu, Fawang; Li, Changpin; Burrage, Kevin; Turner, Ian; Anh, V.
2014
Fourier spectral methods for fractional-in-space reaction-diffusion equations. Zbl 1306.65265
Bueno-Orovio, Alfonso; Kay, David; Burrage, Kevin
2014
Stability criteria for implicit Runge-Kutta methods. Zbl 0396.65043
Burrage, Kevin; Butcher, J. C.
1979
Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term. Zbl 1170.65107
Liu, F.; Yang, C.; Burrage, K.
2009
Non-linear stability of a general class of differential equation methods. Zbl 0431.65051
Burrage, Kevin; Butcher, J. C.
1980
An efficient implicit FEM scheme for fractional-in-space reaction-diffusion equations. Zbl 1253.65146
Burrage, Kevin; Hale, Nicholas; Kay, David
2012
Numerical methods and analysis for a class of fractional advection-dispersion models. Zbl 1268.65124
Liu, F.; Zhuang, P.; Burrage, K.
2012
Parallel and sequential methods for ordinary differential equations. Zbl 0838.65073
Burrage, Kevin
1995
Finite difference methods and a Fourier analysis for the fractional reaction-subdiffusion equation. Zbl 1144.65057
Chen, Chang-Ming; Liu, F.; Burrage, K.
2008
A new fractional finite volume method for solving the fractional diffusion equation. Zbl 1429.65213
Liu, F.; Zhuang, P.; Turner, I.; Burrage, K.; Anh, V.
2014
Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations on a finite domain. Zbl 1234.35300
Jiang, H.; Liu, F.; Turner, I.; Burrage, K.
2012
Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain. Zbl 1268.35124
Jiang, H.; Liu, Fawang; Turner, I.; Burrage, K.
2012
High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations. Zbl 0868.65101
Burrage, K.; Burrage, P. M.
1996
Numerical methods for strong solutions of stochastic differential equations: An overview. Zbl 1048.65004
Burrage, K.; Burrage, P. M.; Tian, T.
2004
A special family of Runge-Kutta methods for solving stiff differential equations. Zbl 0384.65034
Burrage, Kevin
1978
Order conditions of stochastic Runge–Kutta methods by B-series. Zbl 0983.65006
Burrage, K.; Burrage, P. M.
2000
A semi-alternating direction method for a 2-D fractional Fitzhugh-Nagumo monodomain model on an approximate irregular domain. Zbl 1349.65316
Liu, Fawang; Zhuang, P.; Turner, I.; Anh, V.; Burrage, K.
2015
An implementation of singly-implicit Runge-Kutta methods. Zbl 0456.65040
Burrage, K.; Butcher, J. C.; Chipman, F. H.
1980
Restarted GMRES preconditioned by deflation. Zbl 0854.65025
Erhel, Jocelyne; Burrage, Kevin; Pohl, Bert
1996
Stochastic delay differential equations for genetic regulatory networks. Zbl 1112.92029
Tian, Tianhai; Burrage, Kevin; Burrage, Pamela M.; Carletti, Margherita
2007
Novel techniques in parameter estimation for fractional dynamical models arising from biological systems. Zbl 1228.93114
Liu, F.; Burrage, K.
2011
Numerical solutions of stochastic differential equations – implementation and stability issues. Zbl 0971.65003
Burrage, Kevin; Burrage, Pamela; Mitsui, Takemoto
2000
Implicit Taylor methods for stiff stochastic differential equations. Zbl 0983.65007
Tian, Tianhai; Burrage, Kevin
2001
High strong order methods for non-commutative stochastic ordinary differential equation systems and the Magnus formula. Zbl 1194.65023
Burrage, K.; Burrage, P. M.
1999
A stable fast time-stepping method for fractional integral and derivative operators. Zbl 1406.65047
Zeng, Fanhai; Turner, Ian; Burrage, Kevin
2018
Stochastic approaches for modelling in vivo reactions. Zbl 1087.92035
Turner, T. E.; Schnell, S.; Burrage, K.
2004
Numerical simulation of stochastic ordinary differential equations in biomathematical modelling. Zbl 1039.65005
Carletti, M.; Burrage, K.; Burrage, P. M.
2004
A study of B-convergence of Runge-Kutta methods. Zbl 0572.65053
Burrage, K.; Hundsdorfer, W. H.; Verwer, J. G.
1986
A note on the balanced method. Zbl 1116.65004
Alcock, Jamie; Burrage, Kevin
2006
A variable stepsize implementation for stochastic differential equations. Zbl 1034.65003
Burrage, P. M.; Burrage, K.
2002
The composite Euler method for stiff stochastic differential equations. Zbl 0987.65009
Burrage, Kevin; Tian, Tianhai
2001
Fast finite difference approximation for identifying parameters in a two-dimensional space-fractional nonlocal model with variable diffusivity coefficients. Zbl 1382.65290
Chen, Shiping; Liu, Fawang; Jiang, X.; Turner, Ian; Burrage, Kevin
2016
General order conditions for stochastic Runge-Kutta methods for both commuting and non-commuting stochastic ordinary differential equation systems. Zbl 0924.65146
Burrage, K.; Burrage, P. M.
1998
Numerical methods for second-order stochastic differential equations. Zbl 1144.65004
Burrage, Kevin; Lenane, Ian; Lythe, Grant
2007
Multiscale modeling of chemical kinetics via the master equation. Zbl 1153.60370
Macnamara, Shev; Burrage, Kevin; Sidje, Roger B.
2008
A computationally effective alternating direction method for the space and time fractional Bloch-Torrey equation in 3-D. Zbl 1311.65114
Yu, Q.; Liu, F.; Turner, I.; Burrage, K.
2012
Two-stage and three-stage diagonally implicit Runge-Kutta Nyström methods of orders three and four. Zbl 0711.65057
Sharp, P. W.; Fine, J. M.; Burrage, K.
1990
The undirected feedback vertex set problem has a Poly$$(k)$$ kernel. Zbl 1154.68421
Burrage, Kevin; Estivill-Castro, Vladimir; Fellows, Michael; Langston, Michael; Mac, Shev; Rosamond, Frances
2006
On the performance of various adaptive preconditioned GMRES strategies. Zbl 0937.65036
Burrage, K.; Erhel, J.
1998
Numerical solution of time fractional diffusion systems. Zbl 1372.65228
Burrage, Kevin; Cardone, Angelamaria; D’Ambrosio, Raffaele; Paternoster, Beatrice
2017
Low rank Runge-Kutta methods, symplecticity and stochastic Hamiltonian problems with additive noise. Zbl 1245.65007
Burrage, Kevin; Burrage, Pamela M.
2012
Stability and convergence of an implicit numerical method for the space and time fractional Bloch-Torrey equation. Zbl 1339.65151
Yu, Qiang; Liu, Fawang; Turner, Ian; Burrage, Kevin
2013
Parallel methods for initial value problems. Zbl 0781.65060
Burrage, Kevin
1993
Efficient block predictor-corrector methods with a small number of corrections. Zbl 0782.65088
Burrage, Kevin
1993
Implicit stochastic Runge-Kutta methods for stochastic differential equations. Zbl 1048.65005
Burrage, Kevin; Tian, Tianhai
2004
Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media. Zbl 1369.35105
Chen, S.; Liu, F.; Burrage, K.
2014
Efficiently implementable algebraically stable Runge-Kutta methods. Zbl 0483.65040
Burrage, Kevin
1982
Structure-preserving Runge-Kutta methods for stochastic Hamiltonian equations with additive noise. Zbl 1291.65017
Burrage, Pamela M.; Burrage, Kevin
2014
Numerical analysis for a variable-order nonlinear cable equation. Zbl 1243.65103
Chen, Chang-Ming; Liu, F.; Burrage, K.
2011
Adams-type methods for the numerical solution of stochastic ordinary differential equations. Zbl 0963.65004
Brugnano, L.; Burrage, K.; Burrage, P. M.
2000
Runge-Kutta methods for stochastic differential equations. Zbl 0824.65148
Burrage, K.; Platen, E.
1994
High order algebraically stable multistep Runge-Kutta methods. Zbl 0611.65046
Burrage, K.
1987
Order properties of implicit multivalue methods for ordinary differential equations. Zbl 0637.65066
Burrage, Kevin
1988
Inexact uniformization method for computing transient distributions of Markov chains. Zbl 1154.65300
Sidje, Roger B.; Burrage, Kevin; Macnamara, Shev
2007
Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media. Zbl 1362.35319
Chen, S.; Liu, F.; Burrage, K.
2014
Two-stage stochastic Runge-Kutta methods for stochastic differential equations. Zbl 1016.65002
Tian, T. H.; Burrage, K.
2002
A Jacobi waveform relaxation method for ODEs. Zbl 0923.65045
Sand, J.; Burrage, K.
1999
A note on the stability properties of the Euler methods for solving stochastic differential equations. Zbl 0980.60083
Burrage, Kevin; Tian, Tianhai
2000
A high accuracy defect-correction multigrid method for the steady incompressible Navier-Stokes equations. Zbl 0811.65113
Altas, Irfan; Burrage, Kevin
1994
Adaptive stepsize based on control theory for stochastic differential equations. Zbl 1049.65009
Burrage, P. M.; Herdiana, R.; Burrage, K.
2004
Numerical simulation for the three-dimension fractional sub-diffusion equation. Zbl 1429.65179
Chen, J.; Liu, F.; Liu, Q.; Chen, X.; Anh, V.; Turner, I.; Burrage, K.
2014
Numerical simulation of the fractional Bloch equations. Zbl 1291.65224
Yu, Q.; Liu, F.; Turner, I.; Burrage, K.
2014
Numerical methods of the variable-order Rayleigh-Stokes problem for a heated generalized second grade fluid with fractional derivative. Zbl 1330.76092
Chen, Chang-Ming; Liu, F.; Burrage, K.; Chen, Y.
2013
A stochastic exponential Euler scheme for simulation of stiff biochemical reaction systems. Zbl 1307.65011
Komori, Yoshio; Burrage, Kevin
2014
The order of B-convergence of algebraically stable Runge-Kutta methods. Zbl 0629.65075
Burrage, K.; Hundsdorfer, W. H.
1987
High order algebraically stable Runge-Kutta methods. Zbl 0401.65049
Burrage, Kevin
1978
Strong first order $$S$$-ROCK methods for stochastic differential equations. Zbl 1258.65007
Komori, Yoshio; Burrage, Kevin
2013
Some novel techniques of parameter estimation for dynamical models in biological systems. Zbl 1402.92203
Liu, F.; Burrage, K.; Hamilton, N. A.
2013
An investigation of nonlinear time-fractional anomalous diffusion models for simulating transport processes in heterogeneous binary media. Zbl 1452.76227
Feng, Libo; Turner, Ian; Perré, Patrick; Burrage, Kevin
2021
A bound on the maximum strong order of stochastic Runge-Kutta methods for stochastic ordinary differential equations. Zbl 0890.65146
Burrage, K.; Burrage, P. M.; Belward, J. A.
1997
Accurate stationary densities with partitioned numerical methods for stochastic differential equations. Zbl 1197.60068
Burrage, Kevin; Lythe, Grant
2009
A new class of semi-implicit methods with linear complexity for nonlinear fractional differential equations. Zbl 1404.65105
Zeng, Fanhai; Turner, Ian; Burrage, Kevin; Karniadakis, George Em
2018
A boundary preserving numerical algorithm for the Wright-Fisher model with mutation. Zbl 1255.65019
Dangerfield, C. E.; Kay, D.; MacNamara, S.; Burrage, K.
2012
Novel numerical methods for time-space fractional reaction diffusion equations in two dimensions. Zbl 1390.65093
Yang, Qianqian; Moroney, Tim; Burrage, Kevin; Turner, Ian; Liu, Fawang
2010
Efficient multistep methods for tempered fractional calculus: algorithms and simulations. Zbl 07099350
Guo, Ling; Zeng, Fanhai; Turner, Ian; Burrage, Kevin; Karniadakis, George Em
2019
Predictor-corrector methods of Runge-Kutta type for stochastic differential equations. Zbl 1026.60075
Burrage, Kevin; Tian, Tianhai
2002
Order results for mono-implicit Runge-Kutta methods. Zbl 0809.65080
Burrage, K.; Chipman, F. H.; Muir, P. H.
1994
Preconditioning waveform relaxation iterations for differential systems. Zbl 0864.65049
Burrage, K.; Jackiewicz, Z.; Nørsett, S. P.; Renaut, R. A.
1996
A numerical method for the fractional FitzHugh-Nagumo monodomain model. Zbl 1390.65074
Liu, Fawang; Turner, Ian; Ahn, Vo; Yang, Qianqian; Burrage, Kevin
2012
The search for the Holy Grail, or: Predictor-corrector methods for solving ODEIVPs. Zbl 0787.65048
Burrage, Kevin
1993
Parallel iterated methods based on multistep Runge-Kutta methods of Radau type. Zbl 0884.65080
Burrage, K.; Suhartanto, H.
1997
The error behaviour of a general class of predictor-corrector methods. Zbl 0743.65064
Burrage, Kevin
1991
A four-stage index 2 diagonally implicit Runge-Kutta method. Zbl 0993.65088
Williams, Russell; Burrage, Kevin; Cameron, Ian; Kerr, Minnie
2002
On the performance of parallel waveform relaxations for differential systems. Zbl 0855.65074
Burrage, Kevin; Dyke, Carolyn; Pohl, Bert
1996
Simplifying assumptions for the order of partitioned multivalue methods. Zbl 0477.65051
Burrage, Kevin; Moss, Pamela
1980
Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations. Zbl 0991.65005
Burrage, Kevin; Tian, Tianhai
2001
Weak second order S-ROCK methods for Stratonovich stochastic differential equations. Zbl 1238.60063
Komori, Yoshio; Burrage, Kevin
2012
Numerical solution of the time fractional reaction-diffusion equation with a moving boundary. Zbl 1415.65205
Zheng, Minling; Liu, Fawang; Liu, Qingxia; Burrage, Kevin; Simpson, Matthew J.
2017
Weak second order explicit exponential Runge-Kutta methods for stochastic differential equations. Zbl 1387.65064
Komori, Yoshio; Cohen, David; Burrage, Kevin
2017
A deflation technique for linear systems of equations. Zbl 0914.65025
Burrage, K.; Erhel, J.; Pohl, B.; Williams, A.
1998
Stable strong order 1.0 schemes for solving stochastic ordinary differential equations. Zbl 1259.65002
Alcock, Jamie; Burrage, Kevin
2012
On smoothing and order reduction effects for implicit Runge-Kutta formulae. Zbl 0802.65088
Burrage, Kevin; Chan, R. P. K.
1993
Stability and efficiency properties of implicit Runge-Kutta methods. Zbl 0388.65036
Burrage, Kevin
1978
The use of a Riesz fractional differential-based approach for texture enhancement in image processing. Zbl 1386.94018
Yu, Qiang; Liu, Fawang; Turner, Ian; Burrage, Kevin; Vegh, Viktor
2012
Strong predictor-corrector approximation for stochastic delay differential equations. Zbl 1349.65034
Niu, Yuanling; Zhang, Chengjian; Burrage, Kevin
2015
A genetic estimation algorithm for parameters of stochastic ordinary differential equations. Zbl 1429.62362
Alcock, Jamie; Burrage, Kevin
2004
The performance of preconditioned waveform relaxation techniques for pseudospectral methods. Zbl 0863.65063
Burrage, K.; Jackiewicz, Z.; Renaut, R. A.
1996
The stability properties of singly-implicit general linear methods. Zbl 0578.65067
Burrage, K.; Chipman, F. H.
1985
Parallel methods for ODEs. Zbl 0900.65210
Burrage, Kevin
1997
An investigation of nonlinear time-fractional anomalous diffusion models for simulating transport processes in heterogeneous binary media. Zbl 1452.76227
Feng, Libo; Turner, Ian; Perré, Patrick; Burrage, Kevin
2021
A class of new Magnus-type methods for semi-linear non-commutative Itô stochastic differential equations. Zbl 1482.65013
Yang, Guoguo; Burrage, Kevin; Komori, Yoshio; Burrage, Pamela; Ding, Xiaohua
2021
Globally simple heffter arrays $$H ( n ; k )$$ when $$k \equiv 0 , 3 \pmod 4$$. Zbl 1435.05040
Burrage, Kevin; Donovan, Diane M.; Cavenagh, Nicholas J.; Yazıcı, Emine Ş.
2020
Efficient multistep methods for tempered fractional calculus: algorithms and simulations. Zbl 07099350
Guo, Ling; Zeng, Fanhai; Turner, Ian; Burrage, Kevin; Karniadakis, George Em
2019
S-ROCK methods for stochastic delay differential equations with one fixed delay. Zbl 1417.65023
Komori, Yoshio; Eremin, Alexey; Burrage, Kevin
2019
Optimal control of acute myeloid leukaemia. Zbl 1411.92149
Sharp, Jesse A.; Browning, Alexander P.; Mapder, Tarunendu; Burrage, Kevin; Simpson, Matthew J.
2019
Wider contours and adaptive contours. Zbl 07075714
MacNamara, Shev; McLean, William; Burrage, Kevin
2019
A stable fast time-stepping method for fractional integral and derivative operators. Zbl 1406.65047
Zeng, Fanhai; Turner, Ian; Burrage, Kevin
2018
A new class of semi-implicit methods with linear complexity for nonlinear fractional differential equations. Zbl 1404.65105
Zeng, Fanhai; Turner, Ian; Burrage, Kevin; Karniadakis, George Em
2018
Novel analytical and numerical techniques for fractional temporal SEIR measles model. Zbl 1402.92379
Abdullah, F. A.; Liu, F.; Burrage, P.; Burrage, K.; Li, T.
2018
A space-fractional-reaction-diffusion model for pattern formation in coral reefs. Zbl 1426.92007
Somathilake, Lekam Watte; Burrage, Kevin
2018
Estimates of the coverage of parameter space by Latin hypercube and orthogonal array-based sampling. Zbl 1480.62158
Donovan, D.; Burrage, Kevin; Burrage, Pamela; McCourt, T. A.; Thompson, B.; Yazici, E. Ş.
2018
Numerical solution of time fractional diffusion systems. Zbl 1372.65228
Burrage, Kevin; Cardone, Angelamaria; D&rsquo;Ambrosio, Raffaele; Paternoster, Beatrice
2017
Numerical solution of the time fractional reaction-diffusion equation with a moving boundary. Zbl 1415.65205
Zheng, Minling; Liu, Fawang; Liu, Qingxia; Burrage, Kevin; Simpson, Matthew J.
2017
Weak second order explicit exponential Runge-Kutta methods for stochastic differential equations. Zbl 1387.65064
Komori, Yoshio; Cohen, David; Burrage, Kevin
2017
Exact solutions to the fractional time-space Bloch-Torrey equation for magnetic resonance imaging. Zbl 07261219
Bueno-Orovio, Alfonso; Burrage, Kevin
2017
On reflecting boundary conditions for space-fractional equations on a finite interval: proof of the matrix transfer technique. Zbl 1443.35166
Cusimano, Nicole; Burrage, Kevin; Turner, I.; Kay, David
2017
Fast finite difference approximation for identifying parameters in a two-dimensional space-fractional nonlocal model with variable diffusivity coefficients. Zbl 1382.65290
Chen, Shiping; Liu, Fawang; Jiang, X.; Turner, Ian; Burrage, Kevin
2016
Modelling biochemical reaction systems by stochastic differential equations with reflection. Zbl 1343.92165
Niu, Yuanling; Burrage, Kevin; Chen, Luonan
2016
A semi-alternating direction method for a 2-D fractional Fitzhugh-Nagumo monodomain model on an approximate irregular domain. Zbl 1349.65316
Liu, Fawang; Zhuang, P.; Turner, I.; Anh, V.; Burrage, K.
2015
Strong predictor-corrector approximation for stochastic delay differential equations. Zbl 1349.65034
Niu, Yuanling; Zhang, Chengjian; Burrage, Kevin
2015
Application of stochastic phenomenological modelling to cell-to-cell and beat-to-beat electrophysiological variability in cardiac tissue. Zbl 1314.92044
Walmsley, John; Mirams, Gary R.; Pitt-Francis, Joe; Rodriguez, Blanca; Burrage, Kevin
2015
Post-transcriptional regulation in the nucleus and cytoplasm: study of mean time to threshold (MTT) and narrow escape problem. Zbl 1350.92018
Holcman, D.; Duc, K. Dao; Jones, A.; Byrne, H.; Burrage, K.
2015
A Crank-Nicolson ADI spectral method for a two-dimensional Riesz space fractional nonlinear reaction-diffusion equation. Zbl 1382.65349
Zeng, Fanhai; Liu, Fawang; Li, Changpin; Burrage, Kevin; Turner, Ian; Anh, V.
2014
Fourier spectral methods for fractional-in-space reaction-diffusion equations. Zbl 1306.65265
Bueno-Orovio, Alfonso; Kay, David; Burrage, Kevin
2014
A new fractional finite volume method for solving the fractional diffusion equation. Zbl 1429.65213
Liu, F.; Zhuang, P.; Turner, I.; Burrage, K.; Anh, V.
2014
Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media. Zbl 1369.35105
Chen, S.; Liu, F.; Burrage, K.
2014
Structure-preserving Runge-Kutta methods for stochastic Hamiltonian equations with additive noise. Zbl 1291.65017
Burrage, Pamela M.; Burrage, Kevin
2014
Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media. Zbl 1362.35319
Chen, S.; Liu, F.; Burrage, K.
2014
Numerical simulation for the three-dimension fractional sub-diffusion equation. Zbl 1429.65179
Chen, J.; Liu, F.; Liu, Q.; Chen, X.; Anh, V.; Turner, I.; Burrage, K.
2014
Numerical simulation of the fractional Bloch equations. Zbl 1291.65224
Yu, Q.; Liu, F.; Turner, I.; Burrage, K.
2014
A stochastic exponential Euler scheme for simulation of stiff biochemical reaction systems. Zbl 1307.65011
Komori, Yoshio; Burrage, Kevin
2014
Accurate stationary densities with partitioned numerical methods for stochastic partial differential equations. Zbl 1315.65007
Burrage, Kevin; Lythe, Grant
2014
Stability and convergence of an implicit numerical method for the space and time fractional Bloch-Torrey equation. Zbl 1339.65151
Yu, Qiang; Liu, Fawang; Turner, Ian; Burrage, Kevin
2013
Numerical methods of the variable-order Rayleigh-Stokes problem for a heated generalized second grade fluid with fractional derivative. Zbl 1330.76092
Chen, Chang-Ming; Liu, F.; Burrage, K.; Chen, Y.
2013
Strong first order $$S$$-ROCK methods for stochastic differential equations. Zbl 1258.65007
Komori, Yoshio; Burrage, Kevin
2013
Some novel techniques of parameter estimation for dynamical models in biological systems. Zbl 1402.92203
Liu, F.; Burrage, K.; Hamilton, N. A.
2013
A derivative-free explicit method with order 1.0 for solving stochastic delay differential equations. Zbl 1288.65010
Niu, Yuanling; Burrage, Kevin; Zhang, Chengjian
2013
Numerical techniques for simulating a fractional mathematical model of epidermal wound healing. Zbl 1325.92043
Chen, J.; Liu, F.; Burrage, K.; Shen, S.
2013
An efficient implicit FEM scheme for fractional-in-space reaction-diffusion equations. Zbl 1253.65146
Burrage, Kevin; Hale, Nicholas; Kay, David
2012
Numerical methods and analysis for a class of fractional advection-dispersion models. Zbl 1268.65124
Liu, F.; Zhuang, P.; Burrage, K.
2012
Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations on a finite domain. Zbl 1234.35300
Jiang, H.; Liu, F.; Turner, I.; Burrage, K.
2012
Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain. Zbl 1268.35124
Jiang, H.; Liu, Fawang; Turner, I.; Burrage, K.
2012
A computationally effective alternating direction method for the space and time fractional Bloch-Torrey equation in 3-D. Zbl 1311.65114
Yu, Q.; Liu, F.; Turner, I.; Burrage, K.
2012
Low rank Runge-Kutta methods, symplecticity and stochastic Hamiltonian problems with additive noise. Zbl 1245.65007
Burrage, Kevin; Burrage, Pamela M.
2012
A boundary preserving numerical algorithm for the Wright-Fisher model with mutation. Zbl 1255.65019
Dangerfield, C. E.; Kay, D.; MacNamara, S.; Burrage, K.
2012
A numerical method for the fractional FitzHugh-Nagumo monodomain model. Zbl 1390.65074
Liu, Fawang; Turner, Ian; Ahn, Vo; Yang, Qianqian; Burrage, Kevin
2012
Weak second order S-ROCK methods for Stratonovich stochastic differential equations. Zbl 1238.60063
Komori, Yoshio; Burrage, Kevin
2012
Stable strong order 1.0 schemes for solving stochastic ordinary differential equations. Zbl 1259.65002
Alcock, Jamie; Burrage, Kevin
2012
The use of a Riesz fractional differential-based approach for texture enhancement in image processing. Zbl 1386.94018
Yu, Qiang; Liu, Fawang; Turner, Ian; Burrage, Kevin; Vegh, Viktor
2012
Fractional models for the migration of biological cells in complex spatial domains. Zbl 1387.92013
Cusimano, Nicole; Burrage, Kevin; Burrage, Pamela
2012
Novel techniques in parameter estimation for fractional dynamical models arising from biological systems. Zbl 1228.93114
Liu, F.; Burrage, K.
2011
Numerical analysis for a variable-order nonlinear cable equation. Zbl 1243.65103
Chen, Chang-Ming; Liu, F.; Burrage, K.
2011
Supplement: Efficient weak second order stochastic Runge-Kutta methods for non-commutative Stratonovich stochastic differential equations. Zbl 1218.65011
Komori, Yoshio; Burrage, Kevin
2011
Bayes-optimal chemotaxis. Zbl 1208.92008
Mortimer, Duncan; Dayan, Peter; Burrage, Kevin; Goodhill, Geoffrey J.
2011
Novel numerical methods for time-space fractional reaction diffusion equations in two dimensions. Zbl 1390.65093
Yang, Qianqian; Moroney, Tim; Burrage, Kevin; Turner, Ian; Liu, Fawang
2010
Optimizing chemotaxis by measuring unbound-bound transitions. Zbl 1186.92011
Mortimer, Duncan; Dayan, Peter; Burrage, Kevin; Goodhill, Geoffrey J.
2010
Stochastic modeling of naïve T cell homeostasis for competing clonotypes via the master equation. Zbl 1211.92017
MacNamara, Shev; Burrage, Kevin
2010
Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term. Zbl 1170.65107
Liu, F.; Yang, C.; Burrage, K.
2009
Accurate stationary densities with partitioned numerical methods for stochastic differential equations. Zbl 1197.60068
Burrage, Kevin; Lythe, Grant
2009
Spectral approximation of time windows in the solution of dissipative linear differential equations. Zbl 1195.65091
Burrage, K.; Jackiewicz, Z.; Welfert, B. D.
2009
Krylov and steady-state techniques for the solution of the chemical master equation for the mitogen-activated protein kinase cascade. Zbl 1165.92019
MacNamara, Shev; Burrage, Kevin
2009
Opportunistic timing and manipulation in Australian federal elections. Zbl 1157.91331
Lesmono, Dharma; Tonkes, Elliot; Burrage, Kevin
2009
Finite difference methods and a Fourier analysis for the fractional reaction-subdiffusion equation. Zbl 1144.65057
Chen, Chang-Ming; Liu, F.; Burrage, K.
2008
Multiscale modeling of chemical kinetics via the master equation. Zbl 1153.60370
Macnamara, Shev; Burrage, Kevin; Sidje, Roger B.
2008
Fast generalized cross validation using Krylov subspace methods. Zbl 1157.65012
Sidje, Roger B.; Williams, Alan B.; Burrage, Kevin
2008
Stochastic simulation of chemical reactions in spatially complex media. Zbl 1137.92015
Nicolau, Dan V. jun.; Burrage, Kevin
2008
Effects of intrinsic and extrinsic noise can accelerate juxtacrine pattern formation. Zbl 1142.92002
Rudge, Tim; Burrage, Kevin
2008
A note on the existence and uniqueness of a bounded mean-reverting prosess. Zbl 1214.60025
Lesmono, D.; Pollett, P. K.; Tonkes, E. J.; Burrage, K.
2008
Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation. Zbl 1193.76093
Liu, Fawang; Zhuang, P.; Anh, V.; Turner, I.; Burrage, K.
2007
Stochastic delay differential equations for genetic regulatory networks. Zbl 1112.92029
Tian, Tianhai; Burrage, Kevin; Burrage, Pamela M.; Carletti, Margherita
2007
Numerical methods for second-order stochastic differential equations. Zbl 1144.65004
Burrage, Kevin; Lenane, Ian; Lythe, Grant
2007
Inexact uniformization method for computing transient distributions of Markov chains. Zbl 1154.65300
Sidje, Roger B.; Burrage, Kevin; Macnamara, Shev
2007
An improved finite state projection algorithm for the numerical solution of the chemical master equation with applications. Zbl 1334.92475
MacNamara, Shev F.; Burrage, Kevin; Sidje, Roger B.
2007
A note on the balanced method. Zbl 1116.65004
Alcock, Jamie; Burrage, Kevin
2006
The undirected feedback vertex set problem has a Poly$$(k)$$ kernel. Zbl 1154.68421
Burrage, Kevin; Estivill-Castro, Vladimir; Fellows, Michael; Langston, Michael; Mac, Shev; Rosamond, Frances
2006
Accelerated leap methods for simulating discrete stochastic chemical kinetics. Zbl 1132.93345
Burrage, Kevin; Mac, Shev; Tian, Tianhai
2006
QRT: A QR-based tridiagonalization algorithm for nonsymmetric matrices. Zbl 1081.65040
Sidje, Roger B.; Burrage, K.
2005
A continuous time model for election timing. Zbl 1183.91044
Lesmono, D.; Tonkes, E. J.; Burrage, K.
2005
Numerical methods for strong solutions of stochastic differential equations: An overview. Zbl 1048.65004
Burrage, K.; Burrage, P. M.; Tian, T.
2004
Stochastic approaches for modelling in vivo reactions. Zbl 1087.92035
Turner, T. E.; Schnell, S.; Burrage, K.
2004
Numerical simulation of stochastic ordinary differential equations in biomathematical modelling. Zbl 1039.65005
Carletti, M.; Burrage, K.; Burrage, P. M.
2004
Implicit stochastic Runge-Kutta methods for stochastic differential equations. Zbl 1048.65005
Burrage, Kevin; Tian, Tianhai
2004
Adaptive stepsize based on control theory for stochastic differential equations. Zbl 1049.65009
Burrage, P. M.; Herdiana, R.; Burrage, K.
2004
A genetic estimation algorithm for parameters of stochastic ordinary differential equations. Zbl 1429.62362
Alcock, Jamie; Burrage, Kevin
2004
An early political election problem. Zbl 1097.91070
Lesmono, D.; Tonkes, E. J.; Burrage, K.
2004
Bistability and switching in the lysis/lysogeny genetic regulatory network of bacteriophage $$\lambda$$. Zbl 1439.92096
Tian, Tianhai; Burrage, Kevin
2004
On the convergence of LMF-type methods for SODEs. Zbl 1167.65321
Carreras, Giulia; Brugnano, Luigi; Burrage, Kevin
2004
Convergence of the parallel chaotic waveform relaxation method for stiff systems. Zbl 1016.65058
Yuan, Dongjin; Burrage, Kevin
2003
Accuracy issues of Monte-Carlo methods for valuing American options. Zbl 1123.91326
Tian, Tianhai; Burrage, Kevin
2003
A variable stepsize implementation for stochastic differential equations. Zbl 1034.65003
Burrage, P. M.; Burrage, K.
2002
Two-stage stochastic Runge-Kutta methods for stochastic differential equations. Zbl 1016.65002
Tian, T. H.; Burrage, K.
2002
Predictor-corrector methods of Runge-Kutta type for stochastic differential equations. Zbl 1026.60075
Burrage, Kevin; Tian, Tianhai
2002
A four-stage index 2 diagonally implicit Runge-Kutta method. Zbl 0993.65088
Williams, Russell; Burrage, Kevin; Cameron, Ian; Kerr, Minnie
2002
New multivalue methods for differential algebraic equations. Zbl 1055.65101
Kerr, Minnie; Burrage, Kevin
2002
Implicit Taylor methods for stiff stochastic differential equations. Zbl 0983.65007
Tian, Tianhai; Burrage, Kevin
2001
The composite Euler method for stiff stochastic differential equations. Zbl 0987.65009
Burrage, Kevin; Tian, Tianhai
2001
Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations. Zbl 0991.65005
Burrage, Kevin; Tian, Tianhai
2001
Acceleration of convergence of static and dynamic iterations. Zbl 0992.65077
Burrage, K.; Hertono, G.; Jackiewicz, Z.; Welfert, B. D.
2001
Order conditions of stochastic Runge–Kutta methods by B-series. Zbl 0983.65006
Burrage, K.; Burrage, P. M.
2000
...and 57 more Documents
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### Cited by 2,860 Authors

 120 Liu, Fawang 82 Burrage, Kevin 69 Turner, Ian William 47 Anh, Vo V. 35 Jiang, Xiaoyun 31 Dehghan Takht Fooladi, Mehdi 29 Abbaszadeh, Mostafa 27 D’Ambrosio, Raffaele 25 Huang, Chengming 25 Li, Hong 25 Liu, Yang 25 Wang, Hong 24 Butcher, John C. 21 Jackiewicz, Zdzislaw 21 Paternoster, Beatrice 21 Zeng, Fanhai 21 Zhang, Chengjian 20 Gan, Siqing 20 Owolabi, Kolade Matthew 20 Rößler, Andreas 18 Tang, Yifa 17 Cong, Nguyen Huu 17 Feng, Libo 17 Sun, Zhizhong 17 Xiao, Aiguo 17 Zaky, Mahmoud A. 16 Bhrawy, Ali Hassan 16 Jiang, Daqing 14 Brugnano, Luigi 14 Burrage, Pamela M. 14 Cao, Wanrong 14 Fu, Hongfei 14 Hosseini, Seyed Mohammad 14 Karniadakis, George Em 14 Weiner, Rüdiger 13 Băleanu, Dumitru I. 13 Chen, Changming 13 Ding, Xiaohua 13 Li, Changpin 13 Li, Xiaoli 13 Sun, Haiwei 13 Zheng, Xiangcheng 13 Zhuang, Pinghui 12 Conte, Dajana 12 Debrabant, Kristian 12 Hendy, Ahmed S. 12 Li, Shoufu 12 Ma, Qiang 12 Macías-Díaz, Jorge Eduardo 12 Mohebbi, Akbar 12 van der Houwen, Pieter J. 12 Wang, Yuanming 12 Wen, Liping 11 Huang, Ting-Zhu 11 Khaliq, Abdul Q. M. 11 Komori, Yoshio 11 Kvaerno, Anne 11 Lu, Shujuan 11 Mao, Xuerong 11 Sidje, Roger B. 11 Spijker, Marc N. 11 Sun, Hongguang 11 Yang, Qianqian 10 Atangana, Abdon 10 Bu, Weiping 10 González-Pinto, Severiano 10 Gu, Xian-Ming 10 Hairer, Ernst 10 Xu, Da 9 Cardone, Angelamaria 9 Chen, Shanzhen 9 Ding, Hengfei 9 Fan, Zhencheng 9 Hong, Jialin 9 Hundsdorfer, Willem H. 9 Liu, Qun 9 Liu, Zhengguang 9 Tocino, Alicia 9 Wang, Wansheng 9 Wei, LeiLei 9 Yin, Baoli 9 Zhao, Yanmin 9 Zhao, Yongliang 9 Zheng, Liancun 8 Avazzadeh, Zakieh 8 Deng, Weihua 8 Huang, Jianfei 8 Jiang, Yaolin 8 Li, Gongsheng 8 Liu, Huan 8 Mei, Liquan 8 Nie, Yufeng 8 Rui, Hongxing 8 Sandu, Adrian 8 Schneid, Josef 8 Sommeijer, Ben P. 8 Vabishchevich, Pëtr Nikolaevich 8 Wu, Fuke 8 Yu, Qiang 8 Yu, Yuexin ...and 2,760 more Authors
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### Cited in 301 Serials

 220 Journal of Computational and Applied Mathematics 189 Applied Numerical Mathematics 149 Applied Mathematics and Computation 148 Computers & Mathematics with Applications 111 Numerical Algorithms 99 BIT 98 Journal of Computational Physics 80 International Journal of Computer Mathematics 48 Journal of Scientific Computing 39 Advances in Difference Equations 38 Applied Mathematical Modelling 38 Communications in Nonlinear Science and Numerical Simulation 36 SIAM Journal on Scientific Computing 35 Mathematics and Computers in Simulation 35 Numerische Mathematik 34 Computational and Applied Mathematics 28 Chaos, Solitons and Fractals 28 Applied Mathematics Letters 25 Fractional Calculus & Applied Analysis 21 Computer Methods in Applied Mechanics and Engineering 21 Abstract and Applied Analysis 19 Computing 19 SIAM Journal on Numerical Analysis 18 Mathematical Biosciences 18 Physica A 18 Mathematical Problems in Engineering 18 Journal of Applied Mathematics and Computing 17 Engineering Analysis with Boundary Elements 16 Mathematics of Computation 13 Mathematical Methods in the Applied Sciences 13 Advances in Computational Mathematics 12 Advances in Mathematical Physics 12 Communications on Applied Mathematics and Computation 11 Bulletin of Mathematical Biology 11 Stochastic Analysis and Applications 10 Journal of Mathematical Chemistry 10 Advances in Applied Mathematics and Mechanics 10 International Journal of Applied and Computational Mathematics 9 International Journal for Numerical Methods in Engineering 9 Numerical Methods for Partial Differential Equations 9 BIT. Nordisk Tidskrift for Informationsbehandling 9 Journal of Theoretical Biology 8 Computers and Fluids 8 Journal of Mathematical Biology 8 Calcolo 8 Numerical Linear Algebra with Applications 8 Discrete and Continuous Dynamical Systems. Series B 8 Inverse Problems in Science and Engineering 8 Journal of Applied Analysis and Computation 7 Journal of Mathematical Analysis and Applications 7 Numerical Functional Analysis and Optimization 7 Theoretical Computer Science 7 Mathematical and Computer Modelling 7 Computational Mathematics and Mathematical Physics 7 Fractals 7 Discrete Dynamics in Nature and Society 7 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 7 Discrete and Continuous Dynamical Systems. Series S 7 East Asian Journal on Applied Mathematics 7 Journal of Function Spaces 7 AIMS Mathematics 6 Computer Physics Communications 6 Computational Mechanics 6 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 6 Complexity 6 Nonlinear Dynamics 6 Chaos 6 Science China. Mathematics 5 Journal of the Franklin Institute 5 Computational Statistics and Data Analysis 5 Taiwanese Journal of Mathematics 5 Computational Methods in Applied Mathematics 5 Journal of Applied Mathematics 5 Multiscale Modeling & Simulation 5 Boundary Value Problems 5 Nonlinear Analysis. Hybrid Systems 5 International Journal of Differential Equations 4 Applicable Analysis 4 Journal of Mathematical Physics 4 Journal of Statistical Physics 4 SIAM Journal on Discrete Mathematics 4 SIAM Journal on Matrix Analysis and Applications 4 Japan Journal of Industrial and Applied Mathematics 4 Linear Algebra and its Applications 4 SIAM Journal on Applied Mathematics 4 Parallel Algorithms and Applications 4 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 4 Computational Biology and Chemistry 4 Mediterranean Journal of Mathematics 4 International Journal of Numerical Analysis and Modeling 4 Mathematical Biosciences and Engineering 4 Mathematical Modelling of Natural Phenomena 4 Numerical Mathematics: Theory, Methods and Applications 4 Axioms 3 Discrete Mathematics 3 Automatica 3 Journal of Optimization Theory and Applications 3 Acta Mathematicae Applicatae Sinica. English Series 3 Neural Computation 3 Journal of Vibration and Control ...and 201 more Serials
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### Cited in 42 Fields

 1,941 Numerical analysis (65-XX) 941 Partial differential equations (35-XX) 643 Ordinary differential equations (34-XX) 427 Probability theory and stochastic processes (60-XX) 248 Real functions (26-XX) 204 Biology and other natural sciences (92-XX) 167 Fluid mechanics (76-XX) 73 Integral equations (45-XX) 70 Dynamical systems and ergodic theory (37-XX) 69 Systems theory; control (93-XX) 52 Computer science (68-XX) 42 Statistical mechanics, structure of matter (82-XX) 41 Approximations and expansions (41-XX) 39 Operator theory (47-XX) 38 Mechanics of deformable solids (74-XX) 37 Linear and multilinear algebra; matrix theory (15-XX) 36 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 32 Classical thermodynamics, heat transfer (80-XX) 29 Special functions (33-XX) 21 Operations research, mathematical programming (90-XX) 20 Combinatorics (05-XX) 20 Statistics (62-XX) 19 Optics, electromagnetic theory (78-XX) 18 Harmonic analysis on Euclidean spaces (42-XX) 16 Mechanics of particles and systems (70-XX) 15 Difference and functional equations (39-XX) 15 Quantum theory (81-XX) 14 Integral transforms, operational calculus (44-XX) 13 Calculus of variations and optimal control; optimization (49-XX) 10 Geophysics (86-XX) 8 History and biography (01-XX) 8 Functional analysis (46-XX) 8 Information and communication theory, circuits (94-XX) 4 General and overarching topics; collections (00-XX) 4 Number theory (11-XX) 4 Global analysis, analysis on manifolds (58-XX) 3 Topological groups, Lie groups (22-XX) 2 Nonassociative rings and algebras (17-XX) 2 Potential theory (31-XX) 2 Mathematics education (97-XX) 1 General topology (54-XX) 1 Relativity and gravitational theory (83-XX)