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Burrage, Kevin

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Author ID: burrage.kevin Recent zbMATH articles by "Burrage, Kevin"
Published as: Burrage, K.; Burrage, Kevin
Documents Indexed: 182 Publications since 1978, including 3 Books
Reviewing Activity: 264 Reviews
all top 5

Co-Authors

24 single-authored
27 Liu, Fawang
22 Turner, Ian William
20 Burrage, Pamela M.
15 Tian, Tianhai
9 Sidje, Roger B.
7 Jackiewicz, Zdzislaw
7 MacNamara, Shev F.
6 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 Butcher, John C.
3 Chen, Changming
3 Chen, Shiping
3 Lythe, Grant
3 Suhartanto, Heru
3 Tonkes, E. J.
2 Altas, Irfan
2 Brugnano, Luigi
2 Bueno-Orovio, Alfonso
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 Jiang, Haiwen
2 Karniadakis, George Em
2 Kay, David A.
2 Kerr, Minnie
2 Liu, Qingxia
2 Mac, Shev
2 Moroney, Timothy J.
2 Mortimer, Duncan
2 Piskarëv, S. I.
2 Renaut, Rosemary Anne
2 Simpson, Matthew J.
2 Walmsley, John L.
2 Yang, Qianqian
2 Yazıcı, Emine Şule
2 Zhang, Chengjian
1 Abdullah, Farah Aini
1 Ahn, Vo
1 Baker, Christopher T. H.
1 Bednarz, Tomasz P.
1 Browning, Alexander P.
1 Byrne, Helen Mary
1 Cameron, Ian T.
1 Cardone, Angelamaria
1 Carreras, Giulia
1 Cavenagh, Nicholas J.
1 Chan, Robert Peng Kong
1 Chen, Phoebe
1 Chen, Xuehui
1 Chen, Yunkun
1 Christen, Peter
1 Cohen, David Mordecai
1 D’Ambrosio, Raffaele
1 Dangerfield, Ciara E.
1 Duc, K. Dao
1 Dyke, Carolyn
1 Eldershaw, Craig
1 Eremin, Alexey S.
1 Estivill-Castro, Vladimir
1 Farrell, Troy
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 Jones, A. W. P.
1 Kay, Daniel
1 Kay, David C.
1 Langston, Michael A.
1 Leier, André
1 Lenane, Ian
1 Li, Changpin
1 Li, Tao
1 Mapder, Tarunendu
1 Marquez-Lago, Tatiana T.
...and 45 more Co-Authors
all top 5

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 BIT. Nordisk Tidskrift for Informationsbehandling
6 Journal of Theoretical Biology
5 IMA Journal of Numerical Analysis
5 Numerical Algorithms
5 Applied Mathematical Modelling
5 Advances in Computational Mathematics
4 Journal of Computational Physics
4 Applied Mathematics and Computation
3 Annals of Numerical Mathematics
2 IMA Journal of Applied Mathematics
2 The Australian Mathematical Society Gazette
2 Physica D
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 SIAM Journal on Matrix Analysis and Applications
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 Axioms
1 Stochastic and Partial Differential Equations. Analysis and Computations
1 Cogent Mathematics & Statistics

Publications by Year

Citations contained in zbMATH

151 Publications have been cited 3,152 times in 2,005 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.
225
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.
129
2014
Stability criteria for implicit Runge-Kutta methods. Zbl 0396.65043
Burrage, Kevin; Butcher, J. C.
121
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.
109
2009
Non-linear stability of a general class of differential equation methods. Zbl 0431.65051
Burrage, Kevin; Butcher, J. C.
109
1980
Fourier spectral methods for fractional-in-space reaction-diffusion equations. Zbl 1306.65265
Bueno-Orovio, Alfonso; Kay, David; Burrage, Kevin
103
2014
Parallel and sequential methods for ordinary differential equations. Zbl 0838.65073
Burrage, Kevin
103
1995
An efficient implicit FEM scheme for fractional-in-space reaction-diffusion equations. Zbl 1253.65146
Burrage, Kevin; Hale, Nicholas; Kay, David
85
2012
Finite difference methods and a Fourier analysis for the fractional reaction-subdiffusion equation. Zbl 1144.65057
Chen, Chang-Ming; Liu, F.; Burrage, K.
83
2008
Numerical methods and analysis for a class of fractional advection-dispersion models. Zbl 1268.65124
Liu, F.; Zhuang, P.; Burrage, K.
77
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.
74
2012
A special family of Runge-Kutta methods for solving stiff differential equations. Zbl 0384.65034
Burrage, Kevin
74
1978
Numerical methods for strong solutions of stochastic differential equations: An overview. Zbl 1048.65004
Burrage, K.; Burrage, P. M.; Tian, T.
73
2004
High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations. Zbl 0868.65101
Burrage, K.; Burrage, P. M.
70
1996
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.
61
2012
Order conditions of stochastic Runge–Kutta methods by B-series. Zbl 0983.65006
Burrage, K.; Burrage, P. M.
61
2000
An implementation of singly-implicit Runge-Kutta methods. Zbl 0456.65040
Burrage, K.; Butcher, J. C.; Chipman, F. H.
60
1980
Restarted GMRES preconditioned by deflation. Zbl 0854.65025
Erhel, Jocelyne; Burrage, Kevin; Pohl, Bert
57
1996
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.
56
2015
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.
56
2014
Stochastic delay differential equations for genetic regulatory networks. Zbl 1112.92029
Tian, Tianhai; Burrage, Kevin; Burrage, Pamela M.; Carletti, Margherita
52
2007
Numerical solutions of stochastic differential equations – implementation and stability issues. Zbl 0971.65003
Burrage, Kevin; Burrage, Pamela; Mitsui, Takemoto
40
2000
High strong order methods for non-commutative stochastic ordinary differential equation systems and the Magnus formula. Zbl 1194.65023
Burrage, K.; Burrage, P. M.
40
1999
Stochastic approaches for modelling in vivo reactions. Zbl 1087.92035
Turner, T. E.; Schnell, S.; Burrage, K.
39
2004
Implicit Taylor methods for stiff stochastic differential equations. Zbl 0983.65007
Tian, Tianhai; Burrage, Kevin
37
2001
Numerical simulation of stochastic ordinary differential equations in biomathematical modelling. Zbl 1039.65005
Carletti, M.; Burrage, K.; Burrage, P. M.
36
2004
A study of B-convergence of Runge-Kutta methods. Zbl 0572.65053
Burrage, K.; Hundsdorfer, W. H.; Verwer, J. G.
35
1986
A note on the balanced method. Zbl 1116.65004
Alcock, Jamie; Burrage, Kevin
30
2006
The composite Euler method for stiff stochastic differential equations. Zbl 0987.65009
Burrage, Kevin; Tian, Tianhai
29
2001
A variable stepsize implementation for stochastic differential equations. Zbl 1034.65003
Burrage, P. M.; Burrage, K.
28
2002
Multiscale modeling of chemical kinetics via the master equation. Zbl 1153.60370
Macnamara, Shev; Burrage, Kevin; Sidje, Roger B.
27
2008
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.
27
1998
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.
25
2012
Novel techniques in parameter estimation for fractional dynamical models arising from biological systems. Zbl 1228.93114
Liu, F.; Burrage, K.
25
2011
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.
25
1990
On the performance of various adaptive preconditioned GMRES strategies. Zbl 0937.65036
Burrage, K.; Erhel, J.
23
1998
Efficient block predictor-corrector methods with a small number of corrections. Zbl 0782.65088
Burrage, Kevin
23
1993
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
22
2016
Parallel methods for initial value problems. Zbl 0781.65060
Burrage, Kevin
22
1993
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.
21
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
20
2013
Low rank Runge-Kutta methods, symplecticity and stochastic Hamiltonian problems with additive noise. Zbl 1245.65007
Burrage, Kevin; Burrage, Pamela M.
20
2012
Implicit stochastic Runge-Kutta methods for stochastic differential equations. Zbl 1048.65005
Burrage, Kevin; Tian, Tianhai
20
2004
Efficiently implementable algebraically stable Runge-Kutta methods. Zbl 0483.65040
Burrage, Kevin
20
1982
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
19
2006
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.
18
2014
Numerical methods for second-order stochastic differential equations. Zbl 1144.65004
Burrage, Kevin; Lenane, Ian; Lythe, Grant
18
2007
A note on the stability properties of the Euler methods for solving stochastic differential equations. Zbl 0980.60083
Burrage, Kevin; Tian, Tianhai
17
2000
Runge-Kutta methods for stochastic differential equations. Zbl 0824.65148
Burrage, K.; Platen, E.
17
1994
Numerical analysis for a variable-order nonlinear cable equation. Zbl 1243.65103
Chen, Chang-Ming; Liu, F.; Burrage, K.
16
2011
Adams-type methods for the numerical solution of stochastic ordinary differential equations. Zbl 0963.65004
Brugnano, L.; Burrage, K.; Burrage, P. M.
16
2000
Order properties of implicit multivalue methods for ordinary differential equations. Zbl 0637.65066
Burrage, Kevin
16
1988
High order algebraically stable multistep Runge-Kutta methods. Zbl 0611.65046
Burrage, K.
16
1987
A stable fast time-stepping method for fractional integral and derivative operators. Zbl 1406.65047
Zeng, Fanhai; Turner, Ian; Burrage, Kevin
15
2018
Structure-preserving Runge-Kutta methods for stochastic Hamiltonian equations with additive noise. Zbl 1291.65017
Burrage, Pamela M.; Burrage, Kevin
15
2014
Numerical solution of time fractional diffusion systems. Zbl 1372.65228
Burrage, Kevin; Cardone, Angelamaria; D’Ambrosio, Raffaele; Paternoster, Beatrice
14
2017
Inexact uniformization method for computing transient distributions of Markov chains. Zbl 1154.65300
Sidje, Roger B.; Burrage, Kevin; Macnamara, Shev
14
2007
Adaptive stepsize based on control theory for stochastic differential equations. Zbl 1049.65009
Burrage, P. M.; Herdiana, R.; Burrage, K.
14
2004
Two-stage stochastic Runge-Kutta methods for stochastic differential equations. Zbl 1016.65002
Tian, T. H.; Burrage, K.
14
2002
A Jacobi waveform relaxation method for ODEs. Zbl 0923.65045
Sand, J.; Burrage, K.
14
1999
A high accuracy defect-correction multigrid method for the steady incompressible Navier-Stokes equations. Zbl 0811.65113
Altas, Irfan; Burrage, Kevin
14
1994
High order algebraically stable Runge-Kutta methods. Zbl 0401.65049
Burrage, Kevin
13
1978
Numerical simulation of the fractional Bloch equations. Zbl 1291.65224
Yu, Q.; Liu, F.; Turner, I.; Burrage, K.
12
2014
The order of B-convergence of algebraically stable Runge-Kutta methods. Zbl 0629.65075
Burrage, K.; Hundsdorfer, W. H.
12
1987
Strong first order \(S\)-ROCK methods for stochastic differential equations. Zbl 1258.65007
Komori, Yoshio; Burrage, Kevin
11
2013
The error behaviour of a general class of predictor-corrector methods. Zbl 0743.65064
Burrage, Kevin
11
1991
A boundary preserving numerical algorithm for the Wright-Fisher model with mutation. Zbl 1255.65019
Dangerfield, C. E.; Kay, D.; MacNamara, S.; Burrage, K.
10
2012
Accurate stationary densities with partitioned numerical methods for stochastic differential equations. Zbl 1197.60068
Burrage, Kevin; Lythe, Grant
10
2009
Predictor-corrector methods of Runge-Kutta type for stochastic differential equations. Zbl 1026.60075
Burrage, Kevin; Tian, Tianhai
10
2002
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.
10
1997
Parallel iterated methods based on multistep Runge-Kutta methods of Radau type. Zbl 0884.65080
Burrage, K.; Suhartanto, H.
10
1997
Preconditioning waveform relaxation iterations for differential systems. Zbl 0864.65049
Burrage, K.; Jackiewicz, Z.; Nørsett, S. P.; Renaut, R. A.
10
1996
Order results for mono-implicit Runge-Kutta methods. Zbl 0809.65080
Burrage, K.; Chipman, F. H.; Muir, P. H.
10
1994
The search for the Holy Grail, or: Predictor-corrector methods for solving ODEIVPs. Zbl 0787.65048
Burrage, Kevin
10
1993
Some novel techniques of parameter estimation for dynamical models in biological systems. Zbl 1402.92203
Liu, F.; Burrage, K.; Hamilton, N. A.
9
2013
A numerical method for the fractional FitzHugh-Nagumo monodomain model. Zbl 1390.65074
Liu, Fawang; Turner, Ian; Ahn, Vo; Yang, Qianqian; Burrage, Kevin
9
2012
Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations. Zbl 0991.65005
Burrage, Kevin; Tian, Tianhai
9
2001
On the performance of parallel waveform relaxations for differential systems. Zbl 0855.65074
Burrage, Kevin; Dyke, Carolyn; Pohl, Bert
9
1996
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.
8
2014
A stochastic exponential Euler scheme for simulation of stiff biochemical reaction systems. Zbl 1307.65011
Komori, Yoshio; Burrage, Kevin
8
2014
Weak second order S-ROCK methods for Stratonovich stochastic differential equations. Zbl 1238.60063
Komori, Yoshio; Burrage, Kevin
8
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
8
2010
A four-stage index 2 diagonally implicit Runge-Kutta method. Zbl 0993.65088
Williams, Russell; Burrage, Kevin; Cameron, Ian; Kerr, Minnie
8
2002
A deflation technique for linear systems of equations. Zbl 0914.65025
Burrage, K.; Erhel, J.; Pohl, B.; Williams, A.
8
1998
Simplifying assumptions for the order of partitioned multivalue methods. Zbl 0477.65051
Burrage, Kevin; Moss, Pamela
8
1980
Stable strong order 1.0 schemes for solving stochastic ordinary differential equations. Zbl 1259.65002
Alcock, Jamie; Burrage, Kevin
7
2012
On smoothing and order reduction effects for implicit Runge-Kutta formulae. Zbl 0802.65088
Burrage, Kevin; Chan, R. P. K.
7
1993
Stability and efficiency properties of implicit Runge-Kutta methods. Zbl 0388.65036
Burrage, Kevin
7
1978
A genetic estimation algorithm for parameters of stochastic ordinary differential equations. Zbl 1429.62362
Alcock, Jamie; Burrage, Kevin
6
2004
The performance of preconditioned waveform relaxation techniques for pseudospectral methods. Zbl 0863.65063
Burrage, K.; Jackiewicz, Z.; Renaut, R. A.
6
1996
An adaptive numerical integration code for a chain of transputers. Zbl 0713.65012
Burrage, Kevin
6
1990
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
6
1990
The stability properties of singly-implicit general linear methods. Zbl 0578.65067
Burrage, K.; Chipman, F. H.
6
1985
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.
5
2017
Strong predictor-corrector approximation for stochastic delay differential equations. Zbl 1349.65034
Niu, Yuanling; Zhang, Chengjian; Burrage, Kevin
5
2015
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.
5
2013
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
Accelerated leap methods for simulating discrete stochastic chemical kinetics. Zbl 1132.93345
Burrage, Kevin; Mac, Shev; Tian, Tianhai
5
2006
Parallel methods for ODEs. Zbl 0900.65210
Burrage, Kevin
5
1997
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
4
2018
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.
1
2020
Efficient multistep methods for tempered fractional calculus: algorithms and simulations. Zbl 07099350
Guo, Ling; Zeng, Fanhai; Turner, Ian; Burrage, Kevin; Karniadakis, George Em
3
2019
S-ROCK methods for stochastic delay differential equations with one fixed delay. Zbl 1417.65023
Komori, Yoshio; Eremin, Alexey; 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
15
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
4
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.
1
2018
Numerical solution of time fractional diffusion systems. Zbl 1372.65228
Burrage, Kevin; Cardone, Angelamaria; D’Ambrosio, Raffaele; Paternoster, Beatrice
14
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.
5
2017
Weak second order explicit exponential Runge-Kutta methods for stochastic differential equations. Zbl 1387.65064
Komori, Yoshio; Cohen, David; Burrage, Kevin
4
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
1
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
22
2016
Modelling biochemical reaction systems by stochastic differential equations with reflection. Zbl 1343.92165
Niu, Yuanling; Burrage, Kevin; Chen, Luonan
2
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.
56
2015
Strong predictor-corrector approximation for stochastic delay differential equations. Zbl 1349.65034
Niu, Yuanling; Zhang, Chengjian; Burrage, Kevin
5
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
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
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.
129
2014
Fourier spectral methods for fractional-in-space reaction-diffusion equations. Zbl 1306.65265
Bueno-Orovio, Alfonso; Kay, David; Burrage, Kevin
103
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.
56
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.
21
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.
18
2014
Structure-preserving Runge-Kutta methods for stochastic Hamiltonian equations with additive noise. Zbl 1291.65017
Burrage, Pamela M.; Burrage, Kevin
15
2014
Numerical simulation of the fractional Bloch equations. Zbl 1291.65224
Yu, Q.; Liu, F.; Turner, I.; Burrage, K.
12
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.
8
2014
A stochastic exponential Euler scheme for simulation of stiff biochemical reaction systems. Zbl 1307.65011
Komori, Yoshio; Burrage, Kevin
8
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
20
2013
Strong first order \(S\)-ROCK methods for stochastic differential equations. Zbl 1258.65007
Komori, Yoshio; Burrage, Kevin
11
2013
Some novel techniques of parameter estimation for dynamical models in biological systems. Zbl 1402.92203
Liu, F.; Burrage, K.; Hamilton, N. A.
9
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.
5
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
3
2013
Numerical techniques for simulating a fractional mathematical model of epidermal wound healing. Zbl 1325.92043
Chen, J.; Liu, F.; Burrage, K.; Shen, S.
2
2013
An efficient implicit FEM scheme for fractional-in-space reaction-diffusion equations. Zbl 1253.65146
Burrage, Kevin; Hale, Nicholas; Kay, David
85
2012
Numerical methods and analysis for a class of fractional advection-dispersion models. Zbl 1268.65124
Liu, F.; Zhuang, P.; Burrage, K.
77
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.
74
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.
61
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.
25
2012
Low rank Runge-Kutta methods, symplecticity and stochastic Hamiltonian problems with additive noise. Zbl 1245.65007
Burrage, Kevin; Burrage, Pamela M.
20
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.
10
2012
A numerical method for the fractional FitzHugh-Nagumo monodomain model. Zbl 1390.65074
Liu, Fawang; Turner, Ian; Ahn, Vo; Yang, Qianqian; Burrage, Kevin
9
2012
Weak second order S-ROCK methods for Stratonovich stochastic differential equations. Zbl 1238.60063
Komori, Yoshio; Burrage, Kevin
8
2012
Stable strong order 1.0 schemes for solving stochastic ordinary differential equations. Zbl 1259.65002
Alcock, Jamie; Burrage, Kevin
7
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
4
2012
Fractional models for the migration of biological cells in complex spatial domains. Zbl 1387.92013
Cusimano, Nicole; Burrage, Kevin; Burrage, Pamela
1
2012
Novel techniques in parameter estimation for fractional dynamical models arising from biological systems. Zbl 1228.93114
Liu, F.; Burrage, K.
25
2011
Numerical analysis for a variable-order nonlinear cable equation. Zbl 1243.65103
Chen, Chang-Ming; Liu, F.; Burrage, K.
16
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
8
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
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.
109
2009
Accurate stationary densities with partitioned numerical methods for stochastic differential equations. Zbl 1197.60068
Burrage, Kevin; Lythe, Grant
10
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.
83
2008
Multiscale modeling of chemical kinetics via the master equation. Zbl 1153.60370
Macnamara, Shev; Burrage, Kevin; Sidje, Roger B.
27
2008
Effects of intrinsic and extrinsic noise can accelerate juxtacrine pattern formation. Zbl 1142.92002
Rudge, Tim; Burrage, Kevin
3
2008
Stochastic simulation of chemical reactions in spatially complex media. Zbl 1137.92015
Nicolau, Dan V. jun.; Burrage, Kevin
3
2008
Fast generalized cross validation using Krylov subspace methods. Zbl 1157.65012
Sidje, Roger B.; Williams, Alan B.; Burrage, Kevin
2
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.
225
2007
Stochastic delay differential equations for genetic regulatory networks. Zbl 1112.92029
Tian, Tianhai; Burrage, Kevin; Burrage, Pamela M.; Carletti, Margherita
52
2007
Numerical methods for second-order stochastic differential equations. Zbl 1144.65004
Burrage, Kevin; Lenane, Ian; Lythe, Grant
18
2007
Inexact uniformization method for computing transient distributions of Markov chains. Zbl 1154.65300
Sidje, Roger B.; Burrage, Kevin; Macnamara, Shev
14
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
30
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
19
2006
Accelerated leap methods for simulating discrete stochastic chemical kinetics. Zbl 1132.93345
Burrage, Kevin; Mac, Shev; Tian, Tianhai
5
2006
A continuous time model for election timing. Zbl 1183.91044
Lesmono, D.; Tonkes, E. J.; Burrage, K.
1
2005
QRT: A QR-based tridiagonalization algorithm for nonsymmetric matrices. Zbl 1081.65040
Sidje, Roger B.; 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.
73
2004
Stochastic approaches for modelling in vivo reactions. Zbl 1087.92035
Turner, T. E.; Schnell, S.; Burrage, K.
39
2004
Numerical simulation of stochastic ordinary differential equations in biomathematical modelling. Zbl 1039.65005
Carletti, M.; Burrage, K.; Burrage, P. M.
36
2004
Implicit stochastic Runge-Kutta methods for stochastic differential equations. Zbl 1048.65005
Burrage, Kevin; Tian, Tianhai
20
2004
Adaptive stepsize based on control theory for stochastic differential equations. Zbl 1049.65009
Burrage, P. M.; Herdiana, R.; Burrage, K.
14
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
Bistability and switching in the lysis/lysogeny genetic regulatory network of bacteriophage \(\lambda\). Zbl 1439.92096
Tian, Tianhai; Burrage, Kevin
1
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.
28
2002
Two-stage stochastic Runge-Kutta methods for stochastic differential equations. Zbl 1016.65002
Tian, T. H.; Burrage, K.
14
2002
Predictor-corrector methods of Runge-Kutta type for stochastic differential equations. Zbl 1026.60075
Burrage, Kevin; Tian, Tianhai
10
2002
A four-stage index 2 diagonally implicit Runge-Kutta method. Zbl 0993.65088
Williams, Russell; Burrage, Kevin; Cameron, Ian; Kerr, Minnie
8
2002
New multivalue methods for differential algebraic equations. Zbl 1055.65101
Kerr, Minnie; Burrage, Kevin
1
2002
Implicit Taylor methods for stiff stochastic differential equations. Zbl 0983.65007
Tian, Tianhai; Burrage, Kevin
37
2001
The composite Euler method for stiff stochastic differential equations. Zbl 0987.65009
Burrage, Kevin; Tian, Tianhai
29
2001
Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations. Zbl 0991.65005
Burrage, Kevin; Tian, Tianhai
9
2001
Acceleration of convergence of static and dynamic iterations. Zbl 0992.65077
Burrage, K.; Hertono, G.; Jackiewicz, Z.; Welfert, B. D.
1
2001
Order conditions of stochastic Runge–Kutta methods by B-series. Zbl 0983.65006
Burrage, K.; Burrage, P. M.
61
2000
Numerical solutions of stochastic differential equations – implementation and stability issues. Zbl 0971.65003
Burrage, Kevin; Burrage, Pamela; Mitsui, Takemoto
40
2000
A note on the stability properties of the Euler methods for solving stochastic differential equations. Zbl 0980.60083
Burrage, Kevin; Tian, Tianhai
17
2000
Adams-type methods for the numerical solution of stochastic ordinary differential equations. Zbl 0963.65004
Brugnano, L.; Burrage, K.; Burrage, P. M.
16
2000
Stochastic methods for ill-posed problems. Zbl 0960.65011
Burrage, K.; Piskarev, S.
2
2000
Parallel iterated methods based on variable step-size multistep Runge-Kutta methods of Radau type for stiff problems. Zbl 0949.65073
Burrage, K.; Suhartanto, H.
1
2000
Parallel half-block methods for initial value problems. Zbl 0952.65055
Burrage, Kevin; Tian, Tianhai
1
2000
High strong order methods for non-commutative stochastic ordinary differential equation systems and the Magnus formula. Zbl 1194.65023
Burrage, K.; Burrage, P. M.
40
1999
...and 51 more Documents
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Cited by 2,559 Authors

107 Liu, Fawang
83 Burrage, Kevin
67 Turner, Ian William
39 Anh, Vo V.
28 Jiang, Xiaoyun
27 Dehghan Takht Fooladi, Mehdi
26 Abbaszadeh, Mostafa
24 Butcher, John C.
23 Huang, Chengming
22 D’Ambrosio, Raffaele
20 Wang, Hong
19 Gan, Siqing
19 Jackiewicz, Zdzislaw
19 Rößler, Andreas
17 Cong, Nguyen Huu
17 Paternoster, Beatrice
17 Tang, Yifa
17 Zhang, Chengjian
16 Bhrawy, Ali Hassan
16 Sun, Zhizhong
16 Zeng, Fanhai
15 Karniadakis, George Em
15 Li, Hong
15 Liu, Yang
14 Brugnano, Luigi
14 Feng, Libo
14 Hosseini, Seyed Mohammad
14 Jiang, Daqing
14 Weiner, Rüdiger
14 Xiao, Aiguo
13 Burrage, Pamela M.
13 Li, Changpin
13 Zaky, Mahmoud A.
13 Zhuang, Pinghui
12 Cao, Wanrong
12 Chen, Changming
12 Li, Shoufu
12 Mohebbi, Akbar
12 van der Houwen, Pieter J.
12 Wen, Liping
12 Yang, Qianqian
11 Băleanu, Dumitru I.
11 Debrabant, Kristian
11 Owolabi, Kolade Matthew
11 Sidje, Roger B.
11 Spijker, Marc N.
11 Wang, Yuanming
10 González-Pinto, Severiano
10 Hairer, Ernst
10 Huang, Ting-Zhu
10 Khaliq, Abdul Q. M.
10 Komori, Yoshio
10 Kvaerno, Anne
10 Li, Xiaoli
10 Macías-Díaz, Jorge Eduardo
10 Mao, Xuerong
9 Conte, Dajana
9 Ding, Hengfei
9 Fu, Hongfei
9 Hundsdorfer, Willem H.
9 Zlatev, Zahari
8 Bu, Weiping
8 Cardone, Angelamaria
8 Ezz-Eldien, Samer S.
8 Fan, Zhencheng
8 Gu, Xian-Ming
8 Hong, Jialin
8 Huang, Jianfei
8 Jiang, Yaolin
8 Jimenez, Juan Carlos
8 Liu, Qun
8 Lu, Shujuan
8 Moroney, Timothy J.
8 Mustapha, Kassem
8 Schneid, Josef
8 Sommeijer, Ben P.
8 Sun, Hongguang
8 Tocino, Alicia
8 Wang, Wansheng
8 Wei, LeiLei
8 Wolf, Verena
8 Wu, Fuke
8 Yu, Yuexin
8 Zhang, Hongmei
8 Zhao, Yanmin
8 Zheng, Liancun
7 Atangana, Abdon
7 Bersani, Alberto Maria
7 Buckwar, Evelyn
7 Deng, Weihua
7 Doha, Eid H.
7 Hendy, Ahmed S.
7 Hu, Xiuling
7 Kraaijevanger, J. F. B. M.
7 Liu, Zhengguang
7 Lubich, Christian
7 Nørsett, Syvert Paul
7 Sandu, Adrian
7 Schmitt, Bernhard A.
7 Tian, Tianhai
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Cited in 262 Serials

212 Journal of Computational and Applied Mathematics
176 Applied Numerical Mathematics
132 Computers & Mathematics with Applications
130 Applied Mathematics and Computation
97 Journal of Computational Physics
95 BIT
95 Numerical Algorithms
40 International Journal of Computer Mathematics
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36 Journal of Scientific Computing
35 Numerische Mathematik
30 SIAM Journal on Scientific Computing
24 Communications in Nonlinear Science and Numerical Simulation
24 Advances in Difference Equations
22 Mathematics and Computers in Simulation
22 Computational and Applied Mathematics
21 Mathematical Biosciences
21 Applied Mathematics Letters
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21 Fractional Calculus & Applied Analysis
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18 Mathematical Problems in Engineering
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17 SIAM Journal on Numerical Analysis
16 Mathematics of Computation
15 Engineering Analysis with Boundary Elements
13 Mathematical Methods in the Applied Sciences
13 Chaos, Solitons and Fractals
11 Bulletin of Mathematical Biology
11 Stochastic Analysis and Applications
10 Advances in Computational Mathematics
9 International Journal for Numerical Methods in Engineering
9 Numerical Methods for Partial Differential Equations
9 Journal of Applied Mathematics and Computing
9 BIT. Nordisk Tidskrift for Informationsbehandling
8 Computers and Fluids
8 Journal of Mathematical Biology
8 Physica A
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8 Journal of Mathematical Chemistry
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7 Discrete Dynamics in Nature and Society
7 Advances in Mathematical Physics
7 Communications on Applied Mathematics and Computation
6 Computer Physics Communications
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6 Complexity
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6 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
6 Inverse Problems in Science and Engineering
5 Journal of the Franklin Institute
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5 Computational Statistics and Data Analysis
5 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
5 Discrete and Continuous Dynamical Systems. Series B
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5 International Journal of Differential Equations
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4 SIAM Journal on Discrete Mathematics
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4 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
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4 Computational Biology and Chemistry
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4 Axioms
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3 Applicable Analysis
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3 Physica D
3 Acta Mathematicae Applicatae Sinica. English Series
3 Neural Computation
3 Japan Journal of Industrial and Applied Mathematics
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3 Journal of Vibration and Control
3 Theory of Computing Systems
3 Taiwanese Journal of Mathematics
3 International Journal of Computational Methods
3 Mathematical Biosciences and Engineering
3 Boundary Value Problems
3 Discrete and Continuous Dynamical Systems. Series S
3 Journal of Nonlinear Science and Applications
3 Mathematics
3 SIAM/ASA Journal on Uncertainty Quantification
2 Indian Journal of Pure & Applied Mathematics
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2 ZAMP. Zeitschrift für angewandte Mathematik und Physik
2 The Annals of Probability
2 Automatica
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