Edit Profile (opens in new tab) Burrage, Kevin Co-Author Distance 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: 198 Publications since 1978, including 1 Book and 3 Additional arXiv Preprints 3 Contributions as Editor Reviewing Activity: 280 Reviews Co-Authors: 147 Co-Authors with 176 Joint Publications 3,265 Co-Co-Authors all top 5 Co-Authors 24 single-authored 28 Burrage, Pamela M. 27 Liu, Fawang 25 Turner, Ian William 15 Tian, Tianhai 10 Komori, Yoshio 9 MacNamara, Shev F. 9 Sidje, Roger B. 8 Jackiewicz, Zdzislaw 6 Zeng, Fanhai 5 Anh, Vo V. 5 Bueno-Orovio, Alfonso 5 Chipman, F. H. 5 Pohl, Bert 4 Erhel, Jocelyne 4 Lesmono, Dharma 4 Lythe, Grant 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 Brugnano, Luigi 3 Butcher, John C. 3 Chen, Changming 3 Donovan, Diane M. 3 Lawson, Brodie A. J. 3 Suhartanto, Heru 3 Tonkes, E. J. 3 Weber Dos Santos, Rodrigo 3 Yang, Guoguo 3 Yang, Qianqian 3 Yazıcı, Emine Şule 2 Altas, Irfan 2 Carletti, Margherita 2 Chen, Jinghua 2 Chen, Luonan 2 Cusimano, Nicole 2 Dayan, Peter 2 Ding, Xiaohua 2 Farquhar, Megan E. 2 Feng, Libo 2 Goodhill, Geoffrey J. 2 Herdiana, R. 2 Hundsdorfer, Willem H. 2 Jiang, Hui 2 Karniadakis, George Em 2 Kerr, Minnie 2 Liu, Qingxia 2 Mac, Shev 2 McCourt, Thomas A. 2 Mortimer, Duncan 2 Perré, Patrick 2 Piskarëv, S. I. 2 Renaut, Rosemary Anne 2 Simpson, Matthew J. 2 Somathilake, Lekam Watte 2 Thompson, Harold Bevan 2 Walmsley, John L. 2 Zhang, Chengjian 1 Abdullah, Farah Aini 1 Ahn, Vo 1 Baker, Christopher Thomas Hale 1 Berg, Lucas A. 1 Browning, Alexander P. 1 Cardone, Angelamaria 1 Carreras, Giulia 1 Cavenagh, Nicholas J. 1 Chan, Robert Peng Kong 1 Chen, Phoebe 1 Chen, Shiping 1 Chen, Yunkun 1 Christen, Peter 1 D’Ambrosio, Raffaele 1 Dangerfield, Ciara E. 1 Don, Shamika P. Kekulthotuwage 1 Duc, K. Dao 1 Dyke, Carolyn 1 Eldershaw, Craig 1 Eremin, Alexey S. 1 Estivill-Castro, Vladimir 1 Fellows, Michael Ralph 1 Fine, J. M. 1 Foy, Brody H. 1 Guo, Ling 1 Hale, Nicholas 1 Hamilton, Nicholas A. 1 Hanan, James 1 Hegland, Markus 1 Helmstedt, Kate J. 1 Hertono, G. 1 Holcman, David 1 Iavernaro, Felice 1 Jiang, Xiaoyun 1 Krauskopf, Bernd 1 Langston, Michael A. 1 Leier, André 1 Lenane, Ian ...and 47 more Co-Authors all top 5 Serials 17 Journal of Computational and Applied Mathematics 14 BIT 13 SIAM Journal on Numerical Analysis 13 Applied Numerical Mathematics 13 The ANZIAM Journal 9 Numerical Algorithms 9 SIAM Journal on Scientific Computing 7 Computers & Mathematics with Applications 6 Journal of Computational Physics 6 BIT. Nordisk Tidskrift for Informationsbehandling 6 Journal of Theoretical Biology 5 IMA Journal of Numerical Analysis 5 Applied Mathematics and Computation 5 Advances in Computational Mathematics 4 Applied Mathematical Modelling 4 Communications in Nonlinear Science and Numerical Simulation 3 Journal of Scientific Computing 3 Annals of Numerical Mathematics 2 IMA Journal of Applied Mathematics 2 The Australian Mathematical Society Gazette 2 Physica D 2 Numerical Methods for Partial Differential Equations 2 SIAM Journal on Matrix Analysis and Applications 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 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 all top 5 Fields 155 Numerical analysis (65-XX) 67 Ordinary differential equations (34-XX) 54 Probability theory and stochastic processes (60-XX) 38 Partial differential equations (35-XX) 34 Biology and other natural sciences (92-XX) 12 Real functions (26-XX) 9 Fluid mechanics (76-XX) 5 Dynamical systems and ergodic theory (37-XX) 5 Statistics (62-XX) 4 General and overarching topics; collections (00-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Computer science (68-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Integral equations (45-XX) 3 Mechanics of deformable solids (74-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 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 Geophysics (86-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 167 Publications have been cited 4,656 times in 3,053 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. 339 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. 245 2014 Fourier spectral methods for fractional-in-space reaction-diffusion equations. Zbl 1306.65265 Bueno-Orovio, Alfonso; Kay, David; Burrage, Kevin 199 2014 An efficient implicit FEM scheme for fractional-in-space reaction-diffusion equations. Zbl 1253.65146 Burrage, Kevin; Hale, Nicholas; Kay, David 148 2012 Stability criteria for implicit Runge-Kutta methods. Zbl 0396.65043 Burrage, Kevin; Butcher, J. C. 144 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. 143 2009 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. 141 2014 Numerical methods and analysis for a class of fractional advection-dispersion models. Zbl 1268.65124 Liu, F.; Zhuang, P.; Burrage, K. 127 2012 Parallel and sequential methods for ordinary differential equations. Zbl 0838.65073 Burrage, Kevin 122 1995 Non-linear stability of a general class of differential equation methods. Zbl 0431.65051 Burrage, Kevin; Butcher, J. C. 121 1980 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. 116 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. 113 2012 Finite difference methods and a Fourier analysis for the fractional reaction-subdiffusion equation. Zbl 1144.65057 Chen, Chang-Ming; Liu, F.; Burrage, K. 101 2008 High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations. Zbl 0868.65101 Burrage, K.; Burrage, P. M. 95 1996 Numerical methods for strong solutions of stochastic differential equations: An overview. Zbl 1048.65004 Burrage, K.; Burrage, P. M.; Tian, T. 85 2004 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. 83 2015 Order conditions of stochastic Runge–Kutta methods by B-series. Zbl 0983.65006 Burrage, K.; Burrage, P. M. 80 2000 A special family of Runge-Kutta methods for solving stiff differential equations. Zbl 0384.65034 Burrage, Kevin 79 1978 An implementation of singly-implicit Runge-Kutta methods. Zbl 0456.65040 Burrage, K.; Butcher, J. C.; Chipman, F. H. 69 1980 Restarted GMRES preconditioned by deflation. Zbl 0854.65025 Erhel, Jocelyne; Burrage, Kevin; Pohl, Bert 66 1996 Stochastic delay differential equations for genetic regulatory networks. Zbl 1112.92029 Tian, Tianhai; Burrage, Kevin; Burrage, Pamela M.; Carletti, Margherita 62 2007 Novel techniques in parameter estimation for fractional dynamical models arising from biological systems. Zbl 1228.93114 Liu, F.; Burrage, K. 61 2011 A stable fast time-stepping method for fractional integral and derivative operators. Zbl 1406.65047 Zeng, Fanhai; Turner, Ian; Burrage, Kevin 59 2018 Numerical solutions of stochastic differential equations – implementation and stability issues. Zbl 0971.65003 Burrage, Kevin; Burrage, Pamela; Mitsui, Taketomo 50 2000 Implicit Taylor methods for stiff stochastic differential equations. Zbl 0983.65007 Tian, Tianhai; Burrage, Kevin 50 2001 Stochastic approaches for modelling in vivo reactions. Zbl 1087.92035 Turner, T. E.; Schnell, S.; Burrage, K. 47 2004 High strong order methods for non-commutative stochastic ordinary differential equation systems and the Magnus formula. Zbl 1194.65023 Burrage, K.; Burrage, P. M. 46 1999 A study of B-convergence of Runge-Kutta methods. Zbl 0572.65053 Burrage, K.; Hundsdorfer, W. H.; Verwer, J. G. 42 1986 Numerical simulation of stochastic ordinary differential equations in biomathematical modelling. Zbl 1039.65005 Carletti, M.; Burrage, K.; Burrage, P. M. 41 2004 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. 39 2012 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 39 2016 The composite Euler method for stiff stochastic differential equations. Zbl 0987.65009 Burrage, Kevin; Tian, Tianhai 38 2001 Numerical methods for second-order stochastic differential equations. Zbl 1144.65004 Burrage, Kevin; Lenane, Ian; Lythe, Grant 37 2007 A variable stepsize implementation for stochastic differential equations. Zbl 1034.65003 Burrage, P. M.; Burrage, K. 36 2002 Low rank Runge-Kutta methods, symplecticity and stochastic Hamiltonian problems with additive noise. Zbl 1245.65007 Burrage, Kevin; Burrage, Pamela M. 36 2012 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. 36 1998 A note on the balanced method. Zbl 1116.65004 Alcock, Jamie; Burrage, Kevin 35 2006 Efficient multistep methods for tempered fractional calculus: algorithms and simulations. Zbl 07099350 Guo, Ling; Zeng, Fanhai; Turner, Ian; Burrage, Kevin; Karniadakis, George Em 33 2019 Multiscale modeling of chemical kinetics via the master equation. Zbl 1153.60370 Macnamara, Shev; Burrage, Kevin; Sidje, Roger B. 31 2008 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 31 2006 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. 31 2014 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. 29 1990 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 29 2013 Numerical solution of time fractional diffusion systems. Zbl 1372.65228 Burrage, Kevin; Cardone, Angelamaria; D’Ambrosio, Raffaele; Paternoster, Beatrice 29 2017 Structure-preserving Runge-Kutta methods for stochastic Hamiltonian equations with additive noise. Zbl 1291.65017 Burrage, Pamela M.; Burrage, Kevin 28 2014 On the performance of various adaptive preconditioned GMRES strategies. Zbl 0937.65036 Burrage, K.; Erhel, J. 25 1998 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. 25 2014 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 25 2021 Parallel methods for initial value problems. Zbl 0781.65060 Burrage, Kevin 24 1993 Implicit stochastic Runge-Kutta methods for stochastic differential equations. Zbl 1048.65005 Burrage, Kevin; Tian, Tianhai 22 2004 Efficient block predictor-corrector methods with a small number of corrections. Zbl 0782.65088 Burrage, Kevin 22 1993 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. 22 2014 Inexact uniformization method for computing transient distributions of Markov chains. Zbl 1154.65300 Sidje, Roger B.; Burrage, Kevin; Macnamara, Shev 21 2007 Efficiently implementable algebraically stable Runge-Kutta methods. Zbl 0483.65040 Burrage, Kevin 21 1982 Numerical analysis for a variable-order nonlinear cable equation. Zbl 1243.65103 Chen, Chang-Ming; Liu, F.; Burrage, K. 21 2011 A numerical method for the fractional FitzHugh-Nagumo monodomain model. Zbl 1390.65074 Liu, Fawang; Turner, Ian; Ahn, Vo; Yang, Qianqian; Burrage, Kevin 21 2012 Runge-Kutta methods for stochastic differential equations. Zbl 0824.65148 Burrage, K.; Platen, E. 20 1994 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 20 2018 A note on the stability properties of the Euler methods for solving stochastic differential equations. Zbl 0980.60083 Burrage, Kevin; Tian, Tianhai 20 2000 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. 19 2017 A stochastic exponential Euler scheme for simulation of stiff biochemical reaction systems. Zbl 1307.65011 Komori, Yoshio; Burrage, Kevin 19 2014 Two-stage stochastic Runge-Kutta methods for stochastic differential equations. Zbl 1016.65002 Tian, T. H.; Burrage, K. 19 2002 High order algebraically stable multistep Runge-Kutta methods. Zbl 0611.65046 Burrage, K. 18 1987 Order properties of implicit multivalue methods for ordinary differential equations. Zbl 0637.65066 Burrage, Kevin 18 1988 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. 18 2013 Adams-type methods for the numerical solution of stochastic ordinary differential equations. Zbl 0963.65004 Brugnano, L.; Burrage, K.; Burrage, P. M. 18 2000 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 18 2012 Adaptive stepsize based on control theory for stochastic differential equations. Zbl 1049.65009 Burrage, P. M.; Herdiana, R.; Burrage, K. 17 2004 A Jacobi waveform relaxation method for ODEs. Zbl 0923.65045 Sand, J.; Burrage, K. 17 1999 Some novel techniques of parameter estimation for dynamical models in biological systems. Zbl 1402.92203 Liu, F.; Burrage, K.; Hamilton, N. A. 16 2013 Strong first order \(S\)-ROCK methods for stochastic differential equations. Zbl 1258.65007 Komori, Yoshio; Burrage, Kevin 15 2013 Accurate stationary densities with partitioned numerical methods for stochastic differential equations. Zbl 1197.60068 Burrage, Kevin; Lythe, Grant 15 2009 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. 15 2020 Parallel methods for ODEs. Zbl 0900.65210 Burrage, Kevin 14 1997 Predictor-corrector methods of Runge-Kutta type for stochastic differential equations. Zbl 1026.60075 Burrage, Kevin; Tian, Tianhai 14 2002 Order results for mono-implicit Runge-Kutta methods. Zbl 0809.65080 Burrage, K.; Chipman, F. H.; Muir, P. H. 14 1994 A high accuracy defect-correction multigrid method for the steady incompressible Navier-Stokes equations. Zbl 0811.65113 Altas, Irfan; Burrage, Kevin 14 1994 Numerical simulation of the fractional Bloch equations. Zbl 1291.65224 Yu, Q.; Liu, F.; Turner, I.; Burrage, K. 14 2014 A boundary preserving numerical algorithm for the Wright-Fisher model with mutation. Zbl 1255.65019 Dangerfield, C. E.; Kay, D.; MacNamara, S.; Burrage, K. 13 2012 The order of B-convergence of algebraically stable Runge-Kutta methods. Zbl 0629.65075 Burrage, K.; Hundsdorfer, W. H. 13 1987 High order algebraically stable Runge-Kutta methods. Zbl 0401.65049 Burrage, Kevin 13 1978 Weak second order explicit exponential Runge-Kutta methods for stochastic differential equations. Zbl 1387.65064 Komori, Yoshio; Cohen, David; Burrage, Kevin 13 2017 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 13 2010 Weak second order S-ROCK methods for Stratonovich stochastic differential equations. Zbl 1238.60063 Komori, Yoshio; Burrage, Kevin 12 2012 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. 12 1997 A four-stage index 2 diagonally implicit Runge-Kutta method. Zbl 0993.65088 Williams, Russell; Burrage, Kevin; Cameron, Ian; Kerr, Minnie 11 2002 Preconditioning waveform relaxation iterations for differential systems. Zbl 0864.65049 Burrage, K.; Jackiewicz, Z.; Nørsett, S. P.; Renaut, R. A. 11 1996 On the performance of parallel waveform relaxations for differential systems. Zbl 0855.65074 Burrage, Kevin; Dyke, Carolyn; Pohl, Bert 11 1996 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 11 2017 The error behaviour of a general class of predictor-corrector methods. Zbl 0743.65064 Burrage, Kevin 11 1991 Parallel iterated methods based on multistep Runge-Kutta methods of Radau type. Zbl 0884.65080 Burrage, K.; Suhartanto, H. 10 1997 Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations. Zbl 0991.65005 Burrage, Kevin; Tian, Tianhai 10 2001 The search for the Holy Grail, or: Predictor-corrector methods for solving ODEIVPs. Zbl 0787.65048 Burrage, Kevin 10 1993 On order reduction for Runge-Kutta methods applied to differential/algebraic systems and to stiff systems of ODEs. Zbl 0708.65069 Burrage, Kevin; Petzold, Linda 10 1990 Strong predictor-corrector approximation for stochastic delay differential equations. Zbl 1349.65034 Niu, Yuanling; Zhang, Chengjian; Burrage, Kevin 10 2015 A deflation technique for linear systems of equations. Zbl 0914.65025 Burrage, K.; Erhel, J.; Pohl, B.; Williams, A. 9 1998 Simplifying assumptions for the order of partitioned multivalue methods. Zbl 0477.65051 Burrage, Kevin; Moss, Pamela 9 1980 Exact solutions to the fractional time-space Bloch-Torrey equation for magnetic resonance imaging. Zbl 1510.92110 Bueno-Orovio, Alfonso; Burrage, Kevin 9 2017 Stability and efficiency properties of implicit Runge-Kutta methods. Zbl 0388.65036 Burrage, Kevin 8 1978 Stable strong order 1.0 schemes for solving stochastic ordinary differential equations. Zbl 1259.65002 Alcock, Jamie; Burrage, Kevin 8 2012 Complex-order fractional diffusion in reaction-diffusion systems. Zbl 1509.35339 Bueno-Orovio, Alfonso; Burrage, Kevin 3 2023 The use of a time-fractional transport model for performing computational homogenisation of 2D heterogeneous media exhibiting memory effects. Zbl 07662519 Feng, Libo; Turner, Ian; Perré, Patrick; Burrage, Kevin 2 2023 A meshfree radial basis function method for simulation of multi-dimensional conservation problems. Zbl 07777020 Foy, Brody H.; Burrage, Kevin; Turner, Ian 1 2023 A new class of structure-preserving stochastic exponential Runge-Kutta integrators for stochastic differential equations. Zbl 1504.65019 Yang, Guoguo; Burrage, Kevin; Komori, Yoshio; Ding, Xiaohua 1 2022 Effective numerical methods for simulating diffusion on a spherical surface in three dimensions. Zbl 1503.65010 Burrage, Kevin; Burrage, Pamela M.; Lythe, Grant 1 2022 Graph-based homogenisation for modelling cardiac fibrosis. Zbl 07525124 Farquhar, Megan E.; Burrage, Kevin; Weber Dos Santos, Rodrigo; Bueno-Orovio, Alfonso; Lawson, Brodie A. J. 1 2022 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 25 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 6 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. 15 2020 Efficient multistep methods for tempered fractional calculus: algorithms and simulations. Zbl 07099350 Guo, Ling; Zeng, Fanhai; Turner, Ian; Burrage, Kevin; Karniadakis, George Em 33 2019 S-ROCK methods for stochastic delay differential equations with one fixed delay. Zbl 1417.65023 Komori, Yoshio; Eremin, Alexey; Burrage, Kevin 4 2019 A discrete least squares collocation method for two-dimensional nonlinear time-dependent partial differential equations. Zbl 1452.65284 Zeng, Fanhai; Turner, Ian; Burrage, Kevin; Wright, Stephen J. 4 2019 Optimal control of acute myeloid leukaemia. Zbl 1411.92149 Sharp, Jesse A.; Browning, Alexander P.; Mapder, Tarunendu; Burrage, Kevin; Simpson, Matthew J. 3 2019 Wider contours and adaptive contours. Zbl 07075714 MacNamara, Shev; McLean, William; Burrage, Kevin 1 2019 A stable fast time-stepping method for fractional integral and derivative operators. Zbl 1406.65047 Zeng, Fanhai; Turner, Ian; Burrage, Kevin 59 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 20 2018 A space-fractional-reaction-diffusion model for pattern formation in coral reefs. Zbl 1426.92007 Somathilake, Lekam Watte; Burrage, Kevin 6 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. 6 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. 3 2018 On the analysis of mixed-index time fractional differential equation systems. Zbl 1432.34009 Burrage, Kevin; Burrage, Pamela; Turner, Ian; Zeng, Fanhai 1 2018 Numerical solution of time fractional diffusion systems. Zbl 1372.65228 Burrage, Kevin; Cardone, Angelamaria; D’Ambrosio, Raffaele; Paternoster, Beatrice 29 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. 19 2017 Weak second order explicit exponential Runge-Kutta methods for stochastic differential equations. Zbl 1387.65064 Komori, Yoshio; Cohen, David; Burrage, Kevin 13 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 11 2017 Exact solutions to the fractional time-space Bloch-Torrey equation for magnetic resonance imaging. Zbl 1510.92110 Bueno-Orovio, Alfonso; Burrage, Kevin 9 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 39 2016 Modelling biochemical reaction systems by stochastic differential equations with reflection. Zbl 1343.92165 Niu, Yuanling; Burrage, Kevin; Chen, Luonan 7 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. 83 2015 Strong predictor-corrector approximation for stochastic delay differential equations. Zbl 1349.65034 Niu, Yuanling; Zhang, Chengjian; Burrage, Kevin 10 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. 1 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 1 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. 245 2014 Fourier spectral methods for fractional-in-space reaction-diffusion equations. Zbl 1306.65265 Bueno-Orovio, Alfonso; Kay, David; Burrage, Kevin 199 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. 141 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. 31 2014 Structure-preserving Runge-Kutta methods for stochastic Hamiltonian equations with additive noise. Zbl 1291.65017 Burrage, Pamela M.; Burrage, Kevin 28 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. 25 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. 22 2014 A stochastic exponential Euler scheme for simulation of stiff biochemical reaction systems. Zbl 1307.65011 Komori, Yoshio; Burrage, Kevin 19 2014 Numerical simulation of the fractional Bloch equations. Zbl 1291.65224 Yu, Q.; Liu, F.; Turner, I.; Burrage, K. 14 2014 Accurate stationary densities with partitioned numerical methods for stochastic partial differential equations. Zbl 1315.65007 Burrage, Kevin; Lythe, Grant 1 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 29 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. 18 2013 Some novel techniques of parameter estimation for dynamical models in biological systems. Zbl 1402.92203 Liu, F.; Burrage, K.; Hamilton, N. A. 16 2013 Strong first order \(S\)-ROCK methods for stochastic differential equations. Zbl 1258.65007 Komori, Yoshio; Burrage, Kevin 15 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 5 2013 Numerical techniques for simulating a fractional mathematical model of epidermal wound healing. Zbl 1325.92043 Chen, J.; Liu, F.; Burrage, K.; Shen, S. 4 2013 An efficient implicit FEM scheme for fractional-in-space reaction-diffusion equations. Zbl 1253.65146 Burrage, Kevin; Hale, Nicholas; Kay, David 148 2012 Numerical methods and analysis for a class of fractional advection-dispersion models. Zbl 1268.65124 Liu, F.; Zhuang, P.; Burrage, K. 127 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. 116 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. 113 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. 39 2012 Low rank Runge-Kutta methods, symplecticity and stochastic Hamiltonian problems with additive noise. Zbl 1245.65007 Burrage, Kevin; Burrage, Pamela M. 36 2012 A numerical method for the fractional FitzHugh-Nagumo monodomain model. Zbl 1390.65074 Liu, Fawang; Turner, Ian; Ahn, Vo; Yang, Qianqian; Burrage, Kevin 21 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 18 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. 13 2012 Weak second order S-ROCK methods for Stratonovich stochastic differential equations. Zbl 1238.60063 Komori, Yoshio; Burrage, Kevin 12 2012 Stable strong order 1.0 schemes for solving stochastic ordinary differential equations. Zbl 1259.65002 Alcock, Jamie; Burrage, Kevin 8 2012 Fractional models for the migration of biological cells in complex spatial domains. Zbl 1387.92013 Cusimano, Nicole; Burrage, Kevin; Burrage, Pamela 3 2012 Novel techniques in parameter estimation for fractional dynamical models arising from biological systems. Zbl 1228.93114 Liu, F.; Burrage, K. 61 2011 Numerical analysis for a variable-order nonlinear cable equation. Zbl 1243.65103 Chen, Chang-Ming; Liu, F.; Burrage, K. 21 2011 Supplement: Efficient weak second order stochastic Runge-Kutta methods for non-commutative Stratonovich stochastic differential equations. Zbl 1218.65011 Komori, Yoshio; Burrage, Kevin 5 2011 Bayes-optimal chemotaxis. Zbl 1208.92008 Mortimer, Duncan; Dayan, Peter; Burrage, Kevin; Goodhill, Geoffrey J. 2 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 13 2010 Optimizing chemotaxis by measuring unbound-bound transitions. Zbl 1186.92011 Mortimer, Duncan; Dayan, Peter; Burrage, Kevin; Goodhill, Geoffrey J. 4 2010 Stochastic modeling of naïve T cell homeostasis for competing clonotypes via the master equation. Zbl 1211.92017 MacNamara, Shev; Burrage, Kevin 2 2010 Parameter estimation for a phenomenological model of the cardiac action potential. Zbl 1387.92020 Liu, Fawang; Walmsley, John; Burrage, Kevin 2 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. 143 2009 Accurate stationary densities with partitioned numerical methods for stochastic differential equations. Zbl 1197.60068 Burrage, Kevin; Lythe, Grant 15 2009 Spectral approximation of time windows in the solution of dissipative linear differential equations. Zbl 1195.65091 Burrage, K.; Jackiewicz, Z.; Welfert, B. D. 4 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 3 2009 Opportunistic timing and manipulation in Australian federal elections. Zbl 1157.91331 Lesmono, Dharma; Tonkes, Elliot; Burrage, Kevin 2 2009 Finite difference methods and a Fourier analysis for the fractional reaction-subdiffusion equation. Zbl 1144.65057 Chen, Chang-Ming; Liu, F.; Burrage, K. 101 2008 Multiscale modeling of chemical kinetics via the master equation. Zbl 1153.60370 Macnamara, Shev; Burrage, Kevin; Sidje, Roger B. 31 2008 Stochastic simulation of chemical reactions in spatially complex media. Zbl 1137.92015 Nicolau, Dan V. jun.; Burrage, Kevin 5 2008 Fast generalized cross validation using Krylov subspace methods. Zbl 1157.65012 Sidje, Roger B.; Williams, Alan B.; Burrage, Kevin 3 2008 Effects of intrinsic and extrinsic noise can accelerate juxtacrine pattern formation. Zbl 1142.92002 Rudge, Tim; Burrage, Kevin 3 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. 1 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. 339 2007 Stochastic delay differential equations for genetic regulatory networks. Zbl 1112.92029 Tian, Tianhai; Burrage, Kevin; Burrage, Pamela M.; Carletti, Margherita 62 2007 Numerical methods for second-order stochastic differential equations. Zbl 1144.65004 Burrage, Kevin; Lenane, Ian; Lythe, Grant 37 2007 Inexact uniformization method for computing transient distributions of Markov chains. Zbl 1154.65300 Sidje, Roger B.; Burrage, Kevin; Macnamara, Shev 21 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. 2 2007 A note on the balanced method. Zbl 1116.65004 Alcock, Jamie; Burrage, Kevin 35 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 31 2006 Accelerated leap methods for simulating discrete stochastic chemical kinetics. Zbl 1132.93345 Burrage, Kevin; Mac, Shev; Tian, Tianhai 3 2006 QRT: A QR-based tridiagonalization algorithm for nonsymmetric matrices. Zbl 1081.65040 Sidje, Roger B.; Burrage, K. 2 2005 A continuous time model for election timing. Zbl 1183.91044 Lesmono, D.; Tonkes, E. J.; Burrage, K. 1 2005 Numerical methods for strong solutions of stochastic differential equations: An overview. Zbl 1048.65004 Burrage, K.; Burrage, P. M.; Tian, T. 85 2004 Stochastic approaches for modelling in vivo reactions. Zbl 1087.92035 Turner, T. E.; Schnell, S.; Burrage, K. 47 2004 Numerical simulation of stochastic ordinary differential equations in biomathematical modelling. Zbl 1039.65005 Carletti, M.; Burrage, K.; Burrage, P. M. 41 2004 Implicit stochastic Runge-Kutta methods for stochastic differential equations. Zbl 1048.65005 Burrage, Kevin; Tian, Tianhai 22 2004 Adaptive stepsize based on control theory for stochastic differential equations. Zbl 1049.65009 Burrage, P. M.; Herdiana, R.; Burrage, K. 17 2004 Bistability and switching in the lysis/lysogeny genetic regulatory network of bacteriophage \(\lambda\). Zbl 1439.92096 Tian, Tianhai; Burrage, Kevin 7 2004 A genetic estimation algorithm for parameters of stochastic ordinary differential equations. Zbl 1429.62362 Alcock, Jamie; Burrage, Kevin 6 2004 An early political election problem. Zbl 1097.91070 Lesmono, D.; Tonkes, E. J.; Burrage, K. 2 2004 On the convergence of LMF-type methods for SODEs. Zbl 1167.65321 Carreras, Giulia; Brugnano, Luigi; Burrage, Kevin 1 2004 Accuracy issues of Monte-Carlo methods for valuing American options. Zbl 1123.91326 Tian, Tianhai; Burrage, Kevin 3 2003 Convergence of the parallel chaotic waveform relaxation method for stiff systems. Zbl 1016.65058 Yuan, Dongjin; Burrage, Kevin 2 2003 A variable stepsize implementation for stochastic differential equations. Zbl 1034.65003 Burrage, P. M.; Burrage, K. 36 2002 ...and 67 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 3,614 Authors 148 Liu, Fawang 97 Burrage, Kevin 86 Turner, Ian William 56 Anh, Vo V. 48 Jiang, Xiaoyun 36 Li, Hong 35 Liu, Yang 34 D’Ambrosio, Raffaele 32 Wang, Hong 31 Dehghan Takht Fooladi, Mehdi 29 Abbaszadeh, Mostafa 29 Huang, Chengming 29 Owolabi, Kolade Matthew 26 Feng, Libo 26 Zeng, Fanhai 25 Butcher, John C. 25 Paternoster, Beatrice 24 Zaky, Mahmoud A. 22 Băleanu, Dumitru I. 22 Jackiewicz, Zdzislaw 22 Zhang, Chengjian 22 Zhang, Hui 21 Gan, Siqing 21 Karniadakis, George Em 20 Hendy, Ahmed S. 20 Rößler, Andreas 20 Sun, Zhizhong 20 Tang, Yifa 18 Bhrawy, Ali Hassan 18 Burrage, Pamela M. 17 Cao, Wanrong 17 Cong, Nguyen Huu 17 Li, Xiaoli 17 Xiao, Aiguo 17 Zheng, Xiangcheng 17 Zhuang, Pinghui 16 Brugnano, Luigi 16 Conte, Dajana 16 Ding, Xiaohua 16 Fu, Hongfei 16 Jiang, Daqing 16 Lu, Shujuan 16 Xu, Da 15 Komori, Yoshio 15 Li, Changpin 15 Macías-Díaz, Jorge Eduardo 14 Chen, Changming 14 Hosseini, Seyed Mohammad 14 Sun, Haiwei 14 Wang, Wansheng 14 Weiner, Rüdiger 14 Zhao, Yanmin 13 Avazzadeh, Zakieh 13 Gu, Xian-Ming 13 Huang, Ting-Zhu 13 Li, Shoufu 13 Liu, Zhengguang 13 Ma, Qiang 13 Mao, Xuerong 13 Mohebbi, Akbar 13 van der Houwen, Pieter J. 13 Wang, Yuanming 13 Yin, Baoli 13 Zheng, Liancun 12 Atangana, Abdon 12 Bu, Weiping 12 Cardone, Angelamaria 12 Debrabant, Kristian 12 Heydari, Mohammad Hossein 12 Khaliq, Abdul Qayyum Masud 12 Qiao, Leijie 12 Sidje, Roger B. 12 Wen, Liping 12 Yang, Qianqian 11 Chen, Hu 11 Chen, Shanzhen 11 Ding, Hengfei 11 Doha, Eid H. 11 Ezz-Eldien, Samer S. 11 González-Pinto, Severiano 11 Kvaerno, Anne 11 Machado, José António Tenreiro 11 Spijker, Marc N. 11 Sun, Hongguang 11 Wang, Jinfeng 11 Wei, LeiLei 11 Zhang, Haixiang 11 Zhao, Yongliang 10 Deng, Weihua 10 Hairer, Ernst 10 Jiang, Yaolin 10 Liu, Qingxia 10 Shah, Kamal 10 Wei, Ting 10 Yang, Xuehua 9 Cheng, Aijie 9 Di Giovacchino, Stefano 9 Fan, Zhencheng 9 Hong, Jialin 9 Huang, Jianfei ...and 3,514 more Authors all top 5 Cited in 341 Serials 243 Journal of Computational and Applied Mathematics 211 Applied Numerical Mathematics 185 Computers & Mathematics with Applications 159 Applied Mathematics and Computation 127 Numerical Algorithms 119 Journal of Computational Physics 103 BIT 92 International Journal of Computer Mathematics 69 Communications in Nonlinear Science and Numerical Simulation 67 Mathematical Methods in the Applied Sciences 61 Journal of Scientific Computing 57 Mathematics and Computers in Simulation 54 Numerical Methods for Partial Differential Equations 52 Applied Mathematical Modelling 47 Computational and Applied Mathematics 43 SIAM Journal on Scientific Computing 40 Advances in Difference Equations 36 Numerische Mathematik 33 Chaos, Solitons and Fractals 32 Fractional Calculus & Applied Analysis 30 Computer Methods in Applied Mechanics and Engineering 29 Applied Mathematics Letters 24 SIAM Journal on Numerical Analysis 24 Journal of Applied Mathematics and Computing 23 Mathematical Biosciences 23 Engineering Analysis with Boundary Elements 21 Physica A 21 Mathematical Problems in Engineering 21 Abstract and Applied Analysis 19 Computing 18 Mathematics of Computation 18 Numerical Linear Algebra with Applications 15 Advances in Computational Mathematics 15 Journal of Theoretical Biology 14 Journal of Mathematical Chemistry 14 Journal of Applied Analysis and Computation 14 Communications on Applied Mathematics and Computation 13 Computer Physics Communications 13 Bulletin of Mathematical Biology 13 Advances in Mathematical Physics 12 Calcolo 12 International Journal for Numerical Methods in Engineering 11 Stochastic Analysis and Applications 11 Nonlinear Dynamics 11 Discrete and Continuous Dynamical Systems. 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A 4 Journal of Optimization Theory and Applications 4 SIAM Journal on Discrete Mathematics 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 Computing and Visualization in Science ...and 241 more Serials all top 5 Cited in 44 Fields 2,426 Numerical analysis (65-XX) 1,328 Partial differential equations (35-XX) 714 Ordinary differential equations (34-XX) 506 Probability theory and stochastic processes (60-XX) 400 Real functions (26-XX) 266 Biology and other natural sciences (92-XX) 207 Fluid mechanics (76-XX) 86 Dynamical systems and ergodic theory (37-XX) 84 Integral equations (45-XX) 81 Systems theory; control (93-XX) 67 Computer science (68-XX) 54 Approximations and expansions (41-XX) 51 Operator theory (47-XX) 49 Mechanics of deformable solids (74-XX) 49 Statistical mechanics, structure of matter (82-XX) 49 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 48 Linear and multilinear algebra; matrix theory (15-XX) 39 Special functions (33-XX) 39 Classical thermodynamics, heat transfer (80-XX) 37 Combinatorics (05-XX) 27 Harmonic analysis on Euclidean spaces (42-XX) 27 Calculus of variations and optimal control; optimization (49-XX) 27 Statistics (62-XX) 27 Operations research, mathematical programming (90-XX) 22 Optics, electromagnetic theory (78-XX) 18 Mechanics of particles and systems (70-XX) 18 Quantum theory (81-XX) 17 Integral transforms, operational calculus (44-XX) 13 Difference and functional equations (39-XX) 13 Geophysics (86-XX) 11 Functional analysis (46-XX) 10 Information and communication theory, circuits (94-XX) 8 History and biography (01-XX) 6 Number theory (11-XX) 6 Global analysis, analysis on manifolds (58-XX) 3 General and overarching topics; collections (00-XX) 3 Topological groups, Lie groups (22-XX) 3 Measure and integration (28-XX) 2 Nonassociative rings and algebras (17-XX) 2 Potential theory (31-XX) 2 Relativity and gravitational theory (83-XX) 1 Group theory and generalizations (20-XX) 1 General topology (54-XX) 1 Mathematics education (97-XX) Citations by Year