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Author ID: burrage.kevin Recent zbMATH articles by "Burrage, Kevin"
Published as: Burrage, Kevin; Burrage, K.
Homepage: https://staff.qut.edu.au/staff/kevin.burrage
External Links: MGP · ORCID · Google Scholar · dblp
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.
7 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 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 Langston, Michael A.
1 Leier, André
1 Lenane, Ian
1 Li, Changpin
1 Li, Tianzeng
...and 42 more Co-Authors
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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 SIAM Journal on Scientific Computing
7 Computers & Mathematics with Applications
7 Numerical Algorithms
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 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 Journal of Scientific Computing
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

Publications by Year

Citations contained in zbMATH Open

163 Publications have been cited 4,307 times in 2,803 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.
310
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.
221
2014
Fourier spectral methods for fractional-in-space reaction-diffusion equations. Zbl 1306.65265
Bueno-Orovio, Alfonso; Kay, David; Burrage, Kevin
183
2014
Stability criteria for implicit Runge-Kutta methods. Zbl 0396.65043
Burrage, Kevin; Butcher, J. C.
136
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.
133
2009
An efficient implicit FEM scheme for fractional-in-space reaction-diffusion equations. Zbl 1253.65146
Burrage, Kevin; Hale, Nicholas; Kay, David
128
2012
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.
122
2014
Numerical methods and analysis for a class of fractional advection-dispersion models. Zbl 1268.65124
Liu, F.; Zhuang, P.; Burrage, K.
120
2012
Non-linear stability of a general class of differential equation methods. Zbl 0431.65051
Burrage, Kevin; Butcher, J. C.
118
1980
Parallel and sequential methods for ordinary differential equations. Zbl 0838.65073
Burrage, Kevin
117
1995
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.
105
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.
98
2012
Finite difference methods and a Fourier analysis for the fractional reaction-subdiffusion equation. Zbl 1144.65057
Chen, Chang-Ming; Liu, F.; Burrage, K.
95
2008
High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations. Zbl 0868.65101
Burrage, K.; Burrage, P. M.
91
1996
Numerical methods for strong solutions of stochastic differential equations: An overview. Zbl 1048.65004
Burrage, K.; Burrage, P. M.; Tian, T.
80
2004
Order conditions of stochastic Runge–Kutta methods by B-series. Zbl 0983.65006
Burrage, K.; Burrage, P. M.
75
2000
A special family of Runge-Kutta methods for solving stiff differential equations. Zbl 0384.65034
Burrage, Kevin
75
1978
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.
74
2015
An implementation of singly-implicit Runge-Kutta methods. Zbl 0456.65040
Burrage, K.; Butcher, J. C.; Chipman, F. H.
67
1980
Restarted GMRES preconditioned by deflation. Zbl 0854.65025
Erhel, Jocelyne; Burrage, Kevin; Pohl, Bert
61
1996
Stochastic delay differential equations for genetic regulatory networks. Zbl 1112.92029
Tian, Tianhai; Burrage, Kevin; Burrage, Pamela M.; Carletti, Margherita
56
2007
Novel techniques in parameter estimation for fractional dynamical models arising from biological systems. Zbl 1228.93114
Liu, F.; Burrage, K.
55
2011
A stable fast time-stepping method for fractional integral and derivative operators. Zbl 1406.65047
Zeng, Fanhai; Turner, Ian; Burrage, Kevin
50
2018
Implicit Taylor methods for stiff stochastic differential equations. Zbl 0983.65007
Tian, Tianhai; Burrage, Kevin
49
2001
Numerical solutions of stochastic differential equations – implementation and stability issues. Zbl 0971.65003
Burrage, Kevin; Burrage, Pamela; Mitsui, Taketomo
46
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.
45
1999
Numerical simulation of stochastic ordinary differential equations in biomathematical modelling. Zbl 1039.65005
Carletti, M.; Burrage, K.; Burrage, P. M.
41
2004
Stochastic approaches for modelling in vivo reactions. Zbl 1087.92035
Turner, T. E.; Schnell, S.; Burrage, K.
41
2004
A study of B-convergence of Runge-Kutta methods. Zbl 0572.65053
Burrage, K.; Hundsdorfer, W. H.; Verwer, J. G.
40
1986
The composite Euler method for stiff stochastic differential equations. Zbl 0987.65009
Burrage, Kevin; Tian, Tianhai
37
2001
Numerical methods for second-order stochastic differential equations. Zbl 1144.65004
Burrage, Kevin; Lenane, Ian; Lythe, Grant
36
2007
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
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
36
2016
A variable stepsize implementation for stochastic differential equations. Zbl 1034.65003
Burrage, P. M.; Burrage, K.
36
2002
A note on the balanced method. Zbl 1116.65004
Alcock, Jamie; Burrage, Kevin
35
2006
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.
35
2012
Low rank Runge-Kutta methods, symplecticity and stochastic Hamiltonian problems with additive noise. Zbl 1245.65007
Burrage, Kevin; Burrage, Pamela M.
34
2012
Multiscale modeling of chemical kinetics via the master equation. Zbl 1153.60370
Macnamara, Shev; Burrage, Kevin; Sidje, Roger B.
30
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
29
2006
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
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.
27
2014
Numerical solution of time fractional diffusion systems. Zbl 1372.65228
Burrage, Kevin; Cardone, Angelamaria; D’Ambrosio, Raffaele; Paternoster, Beatrice
27
2017
Structure-preserving Runge-Kutta methods for stochastic Hamiltonian equations with additive noise. Zbl 1291.65017
Burrage, Pamela M.; Burrage, Kevin
27
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
26
2013
Efficient multistep methods for tempered fractional calculus: algorithms and simulations. Zbl 07099350
Guo, Ling; Zeng, Fanhai; Turner, Ian; Burrage, Kevin; Karniadakis, George Em
26
2019
On the performance of various adaptive preconditioned GMRES strategies. Zbl 0937.65036
Burrage, K.; Erhel, J.
25
1998
Parallel methods for initial value problems. Zbl 0781.65060
Burrage, Kevin
23
1993
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.
23
2014
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
Efficiently implementable algebraically stable Runge-Kutta methods. Zbl 0483.65040
Burrage, Kevin
21
1982
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
21
2021
Runge-Kutta methods for stochastic differential equations. Zbl 0824.65148
Burrage, K.; Platen, E.
20
1994
Numerical analysis for a variable-order nonlinear cable equation. Zbl 1243.65103
Chen, Chang-Ming; Liu, F.; Burrage, K.
20
2011
Inexact uniformization method for computing transient distributions of Markov chains. Zbl 1154.65300
Sidje, Roger B.; Burrage, Kevin; Macnamara, Shev
20
2007
Two-stage stochastic Runge-Kutta methods for stochastic differential equations. Zbl 1016.65002
Tian, T. H.; Burrage, K.
19
2002
Order properties of implicit multivalue methods for ordinary differential equations. Zbl 0637.65066
Burrage, Kevin
18
1988
Adams-type methods for the numerical solution of stochastic ordinary differential equations. Zbl 0963.65004
Brugnano, L.; Burrage, K.; Burrage, P. M.
18
2000
High order algebraically stable multistep Runge-Kutta methods. Zbl 0611.65046
Burrage, K.
18
1987
A stochastic exponential Euler scheme for simulation of stiff biochemical reaction systems. Zbl 1307.65011
Komori, Yoshio; Burrage, Kevin
18
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
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
18
2018
A Jacobi waveform relaxation method for ODEs. Zbl 0923.65045
Sand, J.; Burrage, K.
17
1999
A note on the stability properties of the Euler methods for solving stochastic differential equations. Zbl 0980.60083
Burrage, Kevin; Tian, Tianhai
17
2000
Adaptive stepsize based on control theory for stochastic differential equations. Zbl 1049.65009
Burrage, P. M.; Herdiana, R.; Burrage, K.
17
2004
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.
17
2017
A numerical method for the fractional FitzHugh-Nagumo monodomain model. Zbl 1390.65074
Liu, Fawang; Turner, Ian; Ahn, Vo; Yang, Qianqian; Burrage, Kevin
16
2012
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.
16
2013
Some novel techniques of parameter estimation for dynamical models in biological systems. Zbl 1402.92203
Liu, F.; Burrage, K.; Hamilton, N. A.
15
2013
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
Strong first order \(S\)-ROCK methods for stochastic differential equations. Zbl 1258.65007
Komori, Yoshio; Burrage, Kevin
14
2013
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
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 explicit exponential Runge-Kutta methods for stochastic differential equations. Zbl 1387.65064
Komori, Yoshio; Cohen, David; Burrage, Kevin
13
2017
Predictor-corrector methods of Runge-Kutta type for stochastic differential equations. Zbl 1026.60075
Burrage, Kevin; Tian, Tianhai
13
2002
Accurate stationary densities with partitioned numerical methods for stochastic differential equations. Zbl 1197.60068
Burrage, Kevin; Lythe, Grant
13
2009
Weak second order S-ROCK methods for Stratonovich stochastic differential equations. Zbl 1238.60063
Komori, Yoshio; Burrage, Kevin
12
2012
Parallel methods for ODEs. Zbl 0900.65210
Burrage, Kevin
12
1997
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
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
12
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
12
2010
Order results for mono-implicit Runge-Kutta methods. Zbl 0809.65080
Burrage, K.; Chipman, F. H.; Muir, P. H.
12
1994
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
A four-stage index 2 diagonally implicit Runge-Kutta method. Zbl 0993.65088
Williams, Russell; Burrage, Kevin; Cameron, Ian; Kerr, Minnie
11
2002
Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations. Zbl 0991.65005
Burrage, Kevin; Tian, Tianhai
10
2001
The error behaviour of a general class of predictor-corrector methods. Zbl 0743.65064
Burrage, Kevin
10
1991
Parallel iterated methods based on multistep Runge-Kutta methods of Radau type. Zbl 0884.65080
Burrage, K.; Suhartanto, H.
10
1997
The search for the Holy Grail, or: Predictor-corrector methods for solving ODEIVPs. Zbl 0787.65048
Burrage, Kevin
10
1993
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
10
2017
Simplifying assumptions for the order of partitioned multivalue methods. Zbl 0477.65051
Burrage, Kevin; Moss, Pamela
9
1980
A deflation technique for linear systems of equations. Zbl 0914.65025
Burrage, K.; Erhel, J.; Pohl, B.; Williams, A.
9
1998
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
9
1990
Strong predictor-corrector approximation for stochastic delay differential equations. Zbl 1349.65034
Niu, Yuanling; Zhang, Chengjian; Burrage, Kevin
9
2015
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.
9
2020
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
On smoothing and order reduction effects for implicit Runge-Kutta formulae. Zbl 0802.65088
Burrage, Kevin; Chan, R. P. K.
7
1993
Complex-order fractional diffusion in reaction-diffusion systems. Zbl 1509.35339
Bueno-Orovio, Alfonso; Burrage, Kevin
2
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
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
21
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.
9
2020
Efficient multistep methods for tempered fractional calculus: algorithms and simulations. Zbl 07099350
Guo, Ling; Zeng, Fanhai; Turner, Ian; Burrage, Kevin; Karniadakis, George Em
26
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.
3
2019
Optimal control of acute myeloid leukaemia. Zbl 1411.92149
Sharp, Jesse A.; Browning, Alexander P.; Mapder, Tarunendu; Burrage, Kevin; Simpson, Matthew J.
2
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
50
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
18
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.
3
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
Numerical solution of time fractional diffusion systems. Zbl 1372.65228
Burrage, Kevin; Cardone, Angelamaria; D’Ambrosio, Raffaele; Paternoster, Beatrice
27
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.
17
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
10
2017
Exact solutions to the fractional time-space Bloch-Torrey equation for magnetic resonance imaging. Zbl 1510.92110
Bueno-Orovio, Alfonso; Burrage, Kevin
6
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
36
2016
Modelling biochemical reaction systems by stochastic differential equations with reflection. Zbl 1343.92165
Niu, Yuanling; Burrage, Kevin; Chen, Luonan
6
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.
74
2015
Strong predictor-corrector approximation for stochastic delay differential equations. Zbl 1349.65034
Niu, Yuanling; Zhang, Chengjian; Burrage, Kevin
9
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.
221
2014
Fourier spectral methods for fractional-in-space reaction-diffusion equations. Zbl 1306.65265
Bueno-Orovio, Alfonso; Kay, David; Burrage, Kevin
183
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.
122
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.
27
2014
Structure-preserving Runge-Kutta methods for stochastic Hamiltonian equations with additive noise. Zbl 1291.65017
Burrage, Pamela M.; Burrage, Kevin
27
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.
23
2014
A stochastic exponential Euler scheme for simulation of stiff biochemical reaction systems. Zbl 1307.65011
Komori, Yoshio; Burrage, Kevin
18
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
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
26
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.
16
2013
Some novel techniques of parameter estimation for dynamical models in biological systems. Zbl 1402.92203
Liu, F.; Burrage, K.; Hamilton, N. A.
15
2013
Strong first order \(S\)-ROCK methods for stochastic differential equations. Zbl 1258.65007
Komori, Yoshio; Burrage, Kevin
14
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
4
2013
Numerical techniques for simulating a fractional mathematical model of epidermal wound healing. Zbl 1325.92043
Chen, J.; Liu, F.; Burrage, K.; Shen, S.
3
2013
An efficient implicit FEM scheme for fractional-in-space reaction-diffusion equations. Zbl 1253.65146
Burrage, Kevin; Hale, Nicholas; Kay, David
128
2012
Numerical methods and analysis for a class of fractional advection-dispersion models. Zbl 1268.65124
Liu, F.; Zhuang, P.; Burrage, K.
120
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.
105
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.
98
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.
35
2012
Low rank Runge-Kutta methods, symplecticity and stochastic Hamiltonian problems with additive noise. Zbl 1245.65007
Burrage, Kevin; Burrage, Pamela M.
34
2012
A numerical method for the fractional FitzHugh-Nagumo monodomain model. Zbl 1390.65074
Liu, Fawang; Turner, Ian; Ahn, Vo; Yang, Qianqian; Burrage, Kevin
16
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
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
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
2
2012
Novel techniques in parameter estimation for fractional dynamical models arising from biological systems. Zbl 1228.93114
Liu, F.; Burrage, K.
55
2011
Numerical analysis for a variable-order nonlinear cable equation. Zbl 1243.65103
Chen, Chang-Ming; Liu, F.; Burrage, K.
20
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
12
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
1
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.
133
2009
Accurate stationary densities with partitioned numerical methods for stochastic differential equations. Zbl 1197.60068
Burrage, Kevin; Lythe, Grant
13
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.
95
2008
Multiscale modeling of chemical kinetics via the master equation. Zbl 1153.60370
Macnamara, Shev; Burrage, Kevin; Sidje, Roger B.
30
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.
310
2007
Stochastic delay differential equations for genetic regulatory networks. Zbl 1112.92029
Tian, Tianhai; Burrage, Kevin; Burrage, Pamela M.; Carletti, Margherita
56
2007
Numerical methods for second-order stochastic differential equations. Zbl 1144.65004
Burrage, Kevin; Lenane, Ian; Lythe, Grant
36
2007
Inexact uniformization method for computing transient distributions of Markov chains. Zbl 1154.65300
Sidje, Roger B.; Burrage, Kevin; Macnamara, Shev
20
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
29
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.
80
2004
Numerical simulation of stochastic ordinary differential equations in biomathematical modelling. Zbl 1039.65005
Carletti, M.; Burrage, K.; Burrage, P. M.
41
2004
Stochastic approaches for modelling in vivo reactions. Zbl 1087.92035
Turner, T. E.; Schnell, S.; Burrage, K.
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
Convergence of the parallel chaotic waveform relaxation method for stiff systems. Zbl 1016.65058
Yuan, Dongjin; Burrage, Kevin
2
2003
Accuracy issues of Monte-Carlo methods for valuing American options. Zbl 1123.91326
Tian, Tianhai; Burrage, Kevin
2
2003
A variable stepsize implementation for stochastic differential equations. Zbl 1034.65003
Burrage, P. M.; Burrage, K.
36
2002
Two-stage stochastic Runge-Kutta methods for stochastic differential equations. Zbl 1016.65002
Tian, T. H.; Burrage, K.
19
2002
Predictor-corrector methods of Runge-Kutta type for stochastic differential equations. Zbl 1026.60075
Burrage, Kevin; Tian, Tianhai
13
2002
A four-stage index 2 diagonally implicit Runge-Kutta method. Zbl 0993.65088
Williams, Russell; Burrage, Kevin; Cameron, Ian; Kerr, Minnie
11
2002
...and 63 more Documents
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Cited by 3,329 Authors

138 Liu, Fawang
91 Burrage, Kevin
79 Turner, Ian William
53 Anh, Vo V.
43 Jiang, Xiaoyun
35 Li, Hong
34 Liu, Yang
32 D’Ambrosio, Raffaele
31 Dehghan Takht Fooladi, Mehdi
31 Wang, Hong
29 Abbaszadeh, Mostafa
27 Huang, Chengming
27 Owolabi, Kolade Matthew
25 Butcher, John C.
25 Feng, Libo
24 Paternoster, Beatrice
24 Zeng, Fanhai
23 Zaky, Mahmoud A.
22 Jackiewicz, Zdzislaw
22 Zhang, Chengjian
21 Gan, Siqing
20 Rößler, Andreas
20 Tang, Yifa
19 Hendy, Ahmed S.
19 Karniadakis, George Em
19 Zhang, Hui
18 Sun, Zhizhong
17 Burrage, Pamela M.
17 Cong, Nguyen Huu
17 Xiao, Aiguo
16 Bhrawy, Ali Hassan
16 Cao, Wanrong
16 Jiang, Daqing
15 Băleanu, Dumitru I.
15 Ding, Xiaohua
15 Fu, Hongfei
15 Komori, Yoshio
15 Li, Xiaoli
15 Zheng, Xiangcheng
14 Brugnano, Luigi
14 Conte, Dajana
14 Hosseini, Seyed Mohammad
14 Li, Changpin
14 Lu, Shujuan
14 Sun, Haiwei
14 Weiner, Rüdiger
14 Zhao, Yanmin
14 Zhuang, Pinghui
13 Chen, Changming
13 Li, Shoufu
13 Mao, Xuerong
13 Wang, Yuanming
13 Xu, Da
13 Yin, Baoli
12 Debrabant, Kristian
12 Gu, Xian-Ming
12 Huang, Ting-Zhu
12 Khaliq, Abdul Q. M.
12 Ma, Qiang
12 Mohebbi, Akbar
12 van der Houwen, Pieter J.
12 Wang, Wansheng
12 Wen, Liping
11 Atangana, Abdon
11 Bu, Weiping
11 Cardone, Angelamaria
11 Chen, Shanzhen
11 González-Pinto, Severiano
11 Kvaerno, Anne
11 Liu, Zhengguang
11 Sidje, Roger B.
11 Spijker, Marc N.
11 Sun, Hongguang
11 Wang, Jinfeng
11 Wei, LeiLei
11 Yang, Qianqian
11 Zhao, Yongliang
10 Avazzadeh, Zakieh
10 Ding, Hengfei
10 Hairer, Ernst
10 Heydari, Mohammad Hossein
10 Qiao, Leijie
10 Wei, Ting
10 Zheng, Liancun
9 Fan, Zhencheng
9 Hong, Jialin
9 Huang, Jianfei
9 Hundsdorfer, Willem H.
9 Li, Meng
9 Li, Zhiyuan
9 Liu, Huan
9 Liu, Qun
9 Machado, José António Tenreiro
9 Mei, Liquan
9 Rui, Hongxing
9 Wang, Fenling
9 Wang, Yushun
9 Yu, Qiang
9 Zhang, Haixiang
8 Cai, Wenjun
...and 3,229 more Authors
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Cited in 327 Serials

238 Journal of Computational and Applied Mathematics
206 Applied Numerical Mathematics
178 Computers & Mathematics with Applications
154 Applied Mathematics and Computation
122 Numerical Algorithms
113 Journal of Computational Physics
103 BIT
92 International Journal of Computer Mathematics
56 Journal of Scientific Computing
51 Communications in Nonlinear Science and Numerical Simulation
46 Mathematics and Computers in Simulation
43 Applied Mathematical Modelling
43 Computational and Applied Mathematics
40 SIAM Journal on Scientific Computing
40 Advances in Difference Equations
36 Numerische Mathematik
35 Numerical Methods for Partial Differential Equations
33 Chaos, Solitons and Fractals
32 Fractional Calculus & Applied Analysis
29 Applied Mathematics Letters
25 Computer Methods in Applied Mechanics and Engineering
25 Mathematical Methods in the Applied Sciences
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20 Physica A
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19 Mathematical Problems in Engineering
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15 Advances in Computational Mathematics
13 Advances in Mathematical Physics
13 Communications on Applied Mathematics and Computation
12 Bulletin of Mathematical Biology
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11 Calcolo
11 Stochastic Analysis and Applications
11 Nonlinear Dynamics
11 Discrete and Continuous Dynamical Systems. Series B
10 Computer Physics Communications
10 International Journal for Numerical Methods in Engineering
10 Advances in Applied Mathematics and Mechanics
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9 Inverse Problems in Science and Engineering
9 BIT. Nordisk Tidskrift for Informationsbehandling
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8 AIMS Mathematics
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7 Discrete Dynamics in Nature and Society
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6 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
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5 Mathematical Modelling of Natural Phenomena
5 International Journal of Differential Equations
5 Computational Methods for Differential Equations
5 Electronic Research Archive
4 Journal of Mathematical Physics
4 Journal of Statistical Physics
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
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4 Parallel Algorithms and Applications
4 Computing and Visualization in Science
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4 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik
4 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
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4 Differentsial’nye Uravneniya i Protsessy Upravleniya
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