Edit Profile Burrage, Kevin Compute Distance To: Compute Author ID: 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 all top 5 Fields 142 Numerical analysis (65-XX) 65 Ordinary differential equations (34-XX) 50 Probability theory and stochastic processes (60-XX) 33 Partial differential equations (35-XX) 31 Biology and other natural sciences (92-XX) 10 Real functions (26-XX) 9 Fluid mechanics (76-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Statistics (62-XX) 4 Computer science (68-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 General and overarching topics; collections (00-XX) 3 Integral equations (45-XX) 3 Operations research, mathematical programming (90-XX) 2 History and biography (01-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Operator theory (47-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Geophysics (86-XX) 2 Systems theory; control (93-XX) 2 Information and communication theory, circuits (94-XX) 1 Combinatorics (05-XX) 1 Number theory (11-XX) 1 Special functions (33-XX) 1 Approximations and expansions (41-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Mechanics of deformable solids (74-XX) 1 Optics, electromagnetic theory (78-XX) Publications by Year all cited Publications top 5 cited Publications 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 1193.76093Liu, 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 1382.65349Zeng, Fanhai; Liu, Fawang; Li, Changpin; Burrage, Kevin; Turner, Ian; Anh, V. 129 2014 Stability criteria for implicit Runge-Kutta methods. Zbl 0396.65043Burrage, Kevin; Butcher, J. C. 121 1979 Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term. Zbl 1170.65107Liu, F.; Yang, C.; Burrage, K. 109 2009 Non-linear stability of a general class of differential equation methods. Zbl 0431.65051Burrage, Kevin; Butcher, J. C. 109 1980 Fourier spectral methods for fractional-in-space reaction-diffusion equations. Zbl 1306.65265Bueno-Orovio, Alfonso; Kay, David; Burrage, Kevin 103 2014 Parallel and sequential methods for ordinary differential equations. Zbl 0838.65073Burrage, Kevin 103 1995 An efficient implicit FEM scheme for fractional-in-space reaction-diffusion equations. Zbl 1253.65146Burrage, Kevin; Hale, Nicholas; Kay, David 85 2012 Finite difference methods and a Fourier analysis for the fractional reaction-subdiffusion equation. Zbl 1144.65057Chen, Chang-Ming; Liu, F.; Burrage, K. 83 2008 Numerical methods and analysis for a class of fractional advection-dispersion models. Zbl 1268.65124Liu, 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 1234.35300Jiang, H.; Liu, F.; Turner, I.; Burrage, K. 74 2012 A special family of Runge-Kutta methods for solving stiff differential equations. Zbl 0384.65034Burrage, Kevin 74 1978 Numerical methods for strong solutions of stochastic differential equations: An overview. Zbl 1048.65004Burrage, K.; Burrage, P. M.; Tian, T. 73 2004 High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations. Zbl 0868.65101Burrage, K.; Burrage, P. M. 70 1996 Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain. Zbl 1268.35124Jiang, H.; Liu, Fawang; Turner, I.; Burrage, K. 61 2012 Order conditions of stochastic Runge–Kutta methods by B-series. Zbl 0983.65006Burrage, K.; Burrage, P. M. 61 2000 An implementation of singly-implicit Runge-Kutta methods. Zbl 0456.65040Burrage, K.; Butcher, J. C.; Chipman, F. H. 60 1980 Restarted GMRES preconditioned by deflation. Zbl 0854.65025Erhel, 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 1349.65316Liu, Fawang; Zhuang, P.; Turner, I.; Anh, V.; Burrage, K. 56 2015 A new fractional finite volume method for solving the fractional diffusion equation. Zbl 1429.65213Liu, F.; Zhuang, P.; Turner, I.; Burrage, K.; Anh, V. 56 2014 Stochastic delay differential equations for genetic regulatory networks. Zbl 1112.92029Tian, Tianhai; Burrage, Kevin; Burrage, Pamela M.; Carletti, Margherita 52 2007 Numerical solutions of stochastic differential equations – implementation and stability issues. Zbl 0971.65003Burrage, Kevin; Burrage, Pamela; Mitsui, Takemoto 40 2000 High strong order methods for non-commutative stochastic ordinary differential equation systems and the Magnus formula. Zbl 1194.65023Burrage, K.; Burrage, P. M. 40 1999 Stochastic approaches for modelling in vivo reactions. Zbl 1087.92035Turner, T. E.; Schnell, S.; Burrage, K. 39 2004 Implicit Taylor methods for stiff stochastic differential equations. Zbl 0983.65007Tian, Tianhai; Burrage, Kevin 37 2001 Numerical simulation of stochastic ordinary differential equations in biomathematical modelling. Zbl 1039.65005Carletti, M.; Burrage, K.; Burrage, P. M. 36 2004 A study of B-convergence of Runge-Kutta methods. Zbl 0572.65053Burrage, K.; Hundsdorfer, W. H.; Verwer, J. G. 35 1986 A note on the balanced method. Zbl 1116.65004Alcock, Jamie; Burrage, Kevin 30 2006 The composite Euler method for stiff stochastic differential equations. Zbl 0987.65009Burrage, Kevin; Tian, Tianhai 29 2001 A variable stepsize implementation for stochastic differential equations. Zbl 1034.65003Burrage, P. M.; Burrage, K. 28 2002 Multiscale modeling of chemical kinetics via the master equation. Zbl 1153.60370Macnamara, 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 0924.65146Burrage, 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 1311.65114Yu, Q.; Liu, F.; Turner, I.; Burrage, K. 25 2012 Novel techniques in parameter estimation for fractional dynamical models arising from biological systems. Zbl 1228.93114Liu, F.; Burrage, K. 25 2011 Two-stage and three-stage diagonally implicit Runge-Kutta Nyström methods of orders three and four. Zbl 0711.65057Sharp, P. W.; Fine, J. M.; Burrage, K. 25 1990 On the performance of various adaptive preconditioned GMRES strategies. Zbl 0937.65036Burrage, K.; Erhel, J. 23 1998 Efficient block predictor-corrector methods with a small number of corrections. Zbl 0782.65088Burrage, Kevin 23 1993 Fast finite difference approximation for identifying parameters in a two-dimensional space-fractional nonlocal model with variable diffusivity coefficients. Zbl 1382.65290Chen, Shiping; Liu, Fawang; Jiang, X.; Turner, Ian; Burrage, Kevin 22 2016 Parallel methods for initial value problems. Zbl 0781.65060Burrage, Kevin 22 1993 Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media. Zbl 1369.35105Chen, 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 1339.65151Yu, Qiang; Liu, Fawang; Turner, Ian; Burrage, Kevin 20 2013 Low rank Runge-Kutta methods, symplecticity and stochastic Hamiltonian problems with additive noise. Zbl 1245.65007Burrage, Kevin; Burrage, Pamela M. 20 2012 Implicit stochastic Runge-Kutta methods for stochastic differential equations. Zbl 1048.65005Burrage, Kevin; Tian, Tianhai 20 2004 Efficiently implementable algebraically stable Runge-Kutta methods. Zbl 0483.65040Burrage, Kevin 20 1982 The undirected feedback vertex set problem has a Poly\((k)\) kernel. Zbl 1154.68421Burrage, 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 1362.35319Chen, S.; Liu, F.; Burrage, K. 18 2014 Numerical methods for second-order stochastic differential equations. Zbl 1144.65004Burrage, Kevin; Lenane, Ian; Lythe, Grant 18 2007 A note on the stability properties of the Euler methods for solving stochastic differential equations. Zbl 0980.60083Burrage, Kevin; Tian, Tianhai 17 2000 Runge-Kutta methods for stochastic differential equations. Zbl 0824.65148Burrage, K.; Platen, E. 17 1994 Numerical analysis for a variable-order nonlinear cable equation. Zbl 1243.65103Chen, Chang-Ming; Liu, F.; Burrage, K. 16 2011 Adams-type methods for the numerical solution of stochastic ordinary differential equations. Zbl 0963.65004Brugnano, L.; Burrage, K.; Burrage, P. M. 16 2000 Order properties of implicit multivalue methods for ordinary differential equations. Zbl 0637.65066Burrage, Kevin 16 1988 High order algebraically stable multistep Runge-Kutta methods. Zbl 0611.65046Burrage, K. 16 1987 A stable fast time-stepping method for fractional integral and derivative operators. Zbl 1406.65047Zeng, Fanhai; Turner, Ian; Burrage, Kevin 15 2018 Structure-preserving Runge-Kutta methods for stochastic Hamiltonian equations with additive noise. Zbl 1291.65017Burrage, Pamela M.; Burrage, Kevin 15 2014 Numerical solution of time fractional diffusion systems. Zbl 1372.65228Burrage, Kevin; Cardone, Angelamaria; D’Ambrosio, Raffaele; Paternoster, Beatrice 14 2017 Inexact uniformization method for computing transient distributions of Markov chains. Zbl 1154.65300Sidje, Roger B.; Burrage, Kevin; Macnamara, Shev 14 2007 Adaptive stepsize based on control theory for stochastic differential equations. Zbl 1049.65009Burrage, P. M.; Herdiana, R.; Burrage, K. 14 2004 Two-stage stochastic Runge-Kutta methods for stochastic differential equations. Zbl 1016.65002Tian, T. H.; Burrage, K. 14 2002 A Jacobi waveform relaxation method for ODEs. Zbl 0923.65045Sand, J.; Burrage, K. 14 1999 A high accuracy defect-correction multigrid method for the steady incompressible Navier-Stokes equations. Zbl 0811.65113Altas, Irfan; Burrage, Kevin 14 1994 High order algebraically stable Runge-Kutta methods. Zbl 0401.65049Burrage, Kevin 13 1978 Numerical simulation of the fractional Bloch equations. Zbl 1291.65224Yu, Q.; Liu, F.; Turner, I.; Burrage, K. 12 2014 The order of B-convergence of algebraically stable Runge-Kutta methods. Zbl 0629.65075Burrage, K.; Hundsdorfer, W. H. 12 1987 Strong first order \(S\)-ROCK methods for stochastic differential equations. Zbl 1258.65007Komori, Yoshio; Burrage, Kevin 11 2013 The error behaviour of a general class of predictor-corrector methods. Zbl 0743.65064Burrage, Kevin 11 1991 A boundary preserving numerical algorithm for the Wright-Fisher model with mutation. Zbl 1255.65019Dangerfield, C. E.; Kay, D.; MacNamara, S.; Burrage, K. 10 2012 Accurate stationary densities with partitioned numerical methods for stochastic differential equations. Zbl 1197.60068Burrage, Kevin; Lythe, Grant 10 2009 Predictor-corrector methods of Runge-Kutta type for stochastic differential equations. Zbl 1026.60075Burrage, Kevin; Tian, Tianhai 10 2002 A bound on the maximum strong order of stochastic Runge-Kutta methods for stochastic ordinary differential equations. Zbl 0890.65146Burrage, K.; Burrage, P. M.; Belward, J. A. 10 1997 Parallel iterated methods based on multistep Runge-Kutta methods of Radau type. Zbl 0884.65080Burrage, K.; Suhartanto, H. 10 1997 Preconditioning waveform relaxation iterations for differential systems. Zbl 0864.65049Burrage, K.; Jackiewicz, Z.; Nørsett, S. P.; Renaut, R. A. 10 1996 Order results for mono-implicit Runge-Kutta methods. Zbl 0809.65080Burrage, K.; Chipman, F. H.; Muir, P. H. 10 1994 The search for the Holy Grail, or: Predictor-corrector methods for solving ODEIVPs. Zbl 0787.65048Burrage, Kevin 10 1993 Some novel techniques of parameter estimation for dynamical models in biological systems. Zbl 1402.92203Liu, F.; Burrage, K.; Hamilton, N. A. 9 2013 A numerical method for the fractional FitzHugh-Nagumo monodomain model. Zbl 1390.65074Liu, Fawang; Turner, Ian; Ahn, Vo; Yang, Qianqian; Burrage, Kevin 9 2012 Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations. Zbl 0991.65005Burrage, Kevin; Tian, Tianhai 9 2001 On the performance of parallel waveform relaxations for differential systems. Zbl 0855.65074Burrage, Kevin; Dyke, Carolyn; Pohl, Bert 9 1996 Numerical simulation for the three-dimension fractional sub-diffusion equation. Zbl 1429.65179Chen, 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 1307.65011Komori, Yoshio; Burrage, Kevin 8 2014 Weak second order S-ROCK methods for Stratonovich stochastic differential equations. Zbl 1238.60063Komori, Yoshio; Burrage, Kevin 8 2012 Novel numerical methods for time-space fractional reaction diffusion equations in two dimensions. Zbl 1390.65093Yang, Qianqian; Moroney, Tim; Burrage, Kevin; Turner, Ian; Liu, Fawang 8 2010 A four-stage index 2 diagonally implicit Runge-Kutta method. Zbl 0993.65088Williams, Russell; Burrage, Kevin; Cameron, Ian; Kerr, Minnie 8 2002 A deflation technique for linear systems of equations. Zbl 0914.65025Burrage, K.; Erhel, J.; Pohl, B.; Williams, A. 8 1998 Simplifying assumptions for the order of partitioned multivalue methods. Zbl 0477.65051Burrage, Kevin; Moss, Pamela 8 1980 Stable strong order 1.0 schemes for solving stochastic ordinary differential equations. Zbl 1259.65002Alcock, Jamie; Burrage, Kevin 7 2012 On smoothing and order reduction effects for implicit Runge-Kutta formulae. Zbl 0802.65088Burrage, Kevin; Chan, R. P. K. 7 1993 Stability and efficiency properties of implicit Runge-Kutta methods. Zbl 0388.65036Burrage, Kevin 7 1978 A genetic estimation algorithm for parameters of stochastic ordinary differential equations. Zbl 1429.62362Alcock, Jamie; Burrage, Kevin 6 2004 The performance of preconditioned waveform relaxation techniques for pseudospectral methods. Zbl 0863.65063Burrage, K.; Jackiewicz, Z.; Renaut, R. A. 6 1996 An adaptive numerical integration code for a chain of transputers. Zbl 0713.65012Burrage, Kevin 6 1990 On order reduction for Runge-Kutta methods applied to differential/algebraic systems and to stiff systems of ODEs. Zbl 0708.65069Burrage, Kevin; Petzold, Linda 6 1990 The stability properties of singly-implicit general linear methods. Zbl 0578.65067Burrage, K.; Chipman, F. H. 6 1985 Numerical solution of the time fractional reaction-diffusion equation with a moving boundary. Zbl 1415.65205Zheng, Minling; Liu, Fawang; Liu, Qingxia; Burrage, Kevin; Simpson, Matthew J. 5 2017 Strong predictor-corrector approximation for stochastic delay differential equations. Zbl 1349.65034Niu, 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 1330.76092Chen, 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 1218.65011Komori, Yoshio; Burrage, Kevin 5 2011 Accelerated leap methods for simulating discrete stochastic chemical kinetics. Zbl 1132.93345Burrage, Kevin; Mac, Shev; Tian, Tianhai 5 2006 Parallel methods for ODEs. Zbl 0900.65210Burrage, Kevin 5 1997 A new class of semi-implicit methods with linear complexity for nonlinear fractional differential equations. Zbl 1404.65105Zeng, 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 1435.05040Burrage, Kevin; Donovan, Diane M.; Cavenagh, Nicholas J.; Yazıcı, Emine Ş. 1 2020 Efficient multistep methods for tempered fractional calculus: algorithms and simulations. Zbl 07099350Guo, 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 1417.65023Komori, Yoshio; Eremin, Alexey; Burrage, Kevin 1 2019 A stable fast time-stepping method for fractional integral and derivative operators. Zbl 1406.65047Zeng, Fanhai; Turner, Ian; Burrage, Kevin 15 2018 A new class of semi-implicit methods with linear complexity for nonlinear fractional differential equations. Zbl 1404.65105Zeng, Fanhai; Turner, Ian; Burrage, Kevin; Karniadakis, George Em 4 2018 Novel analytical and numerical techniques for fractional temporal SEIR measles model. Zbl 1402.92379Abdullah, F. A.; Liu, F.; Burrage, P.; Burrage, K.; Li, T. 1 2018 Numerical solution of time fractional diffusion systems. Zbl 1372.65228Burrage, Kevin; Cardone, Angelamaria; D’Ambrosio, Raffaele; Paternoster, Beatrice 14 2017 Numerical solution of the time fractional reaction-diffusion equation with a moving boundary. Zbl 1415.65205Zheng, 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 1387.65064Komori, 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 1443.35166Cusimano, 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 1382.65290Chen, Shiping; Liu, Fawang; Jiang, X.; Turner, Ian; Burrage, Kevin 22 2016 Modelling biochemical reaction systems by stochastic differential equations with reflection. Zbl 1343.92165Niu, 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 1349.65316Liu, Fawang; Zhuang, P.; Turner, I.; Anh, V.; Burrage, K. 56 2015 Strong predictor-corrector approximation for stochastic delay differential equations. Zbl 1349.65034Niu, 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 1314.92044Walmsley, 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 1350.92018Holcman, 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 1382.65349Zeng, Fanhai; Liu, Fawang; Li, Changpin; Burrage, Kevin; Turner, Ian; Anh, V. 129 2014 Fourier spectral methods for fractional-in-space reaction-diffusion equations. Zbl 1306.65265Bueno-Orovio, Alfonso; Kay, David; Burrage, Kevin 103 2014 A new fractional finite volume method for solving the fractional diffusion equation. Zbl 1429.65213Liu, 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 1369.35105Chen, 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 1362.35319Chen, S.; Liu, F.; Burrage, K. 18 2014 Structure-preserving Runge-Kutta methods for stochastic Hamiltonian equations with additive noise. Zbl 1291.65017Burrage, Pamela M.; Burrage, Kevin 15 2014 Numerical simulation of the fractional Bloch equations. Zbl 1291.65224Yu, Q.; Liu, F.; Turner, I.; Burrage, K. 12 2014 Numerical simulation for the three-dimension fractional sub-diffusion equation. Zbl 1429.65179Chen, 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 1307.65011Komori, Yoshio; Burrage, Kevin 8 2014 Accurate stationary densities with partitioned numerical methods for stochastic partial differential equations. Zbl 1315.65007Burrage, Kevin; Lythe, Grant 1 2014 Stability and convergence of an implicit numerical method for the space and time fractional Bloch-Torrey equation. Zbl 1339.65151Yu, Qiang; Liu, Fawang; Turner, Ian; Burrage, Kevin 20 2013 Strong first order \(S\)-ROCK methods for stochastic differential equations. Zbl 1258.65007Komori, Yoshio; Burrage, Kevin 11 2013 Some novel techniques of parameter estimation for dynamical models in biological systems. Zbl 1402.92203Liu, 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 1330.76092Chen, 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 1288.65010Niu, Yuanling; Burrage, Kevin; Zhang, Chengjian 3 2013 Numerical techniques for simulating a fractional mathematical model of epidermal wound healing. Zbl 1325.92043Chen, J.; Liu, F.; Burrage, K.; Shen, S. 2 2013 An efficient implicit FEM scheme for fractional-in-space reaction-diffusion equations. Zbl 1253.65146Burrage, Kevin; Hale, Nicholas; Kay, David 85 2012 Numerical methods and analysis for a class of fractional advection-dispersion models. Zbl 1268.65124Liu, 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 1234.35300Jiang, 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 1268.35124Jiang, 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 1311.65114Yu, Q.; Liu, F.; Turner, I.; Burrage, K. 25 2012 Low rank Runge-Kutta methods, symplecticity and stochastic Hamiltonian problems with additive noise. Zbl 1245.65007Burrage, Kevin; Burrage, Pamela M. 20 2012 A boundary preserving numerical algorithm for the Wright-Fisher model with mutation. Zbl 1255.65019Dangerfield, C. E.; Kay, D.; MacNamara, S.; Burrage, K. 10 2012 A numerical method for the fractional FitzHugh-Nagumo monodomain model. Zbl 1390.65074Liu, Fawang; Turner, Ian; Ahn, Vo; Yang, Qianqian; Burrage, Kevin 9 2012 Weak second order S-ROCK methods for Stratonovich stochastic differential equations. Zbl 1238.60063Komori, Yoshio; Burrage, Kevin 8 2012 Stable strong order 1.0 schemes for solving stochastic ordinary differential equations. Zbl 1259.65002Alcock, Jamie; Burrage, Kevin 7 2012 The use of a Riesz fractional differential-based approach for texture enhancement in image processing. Zbl 1386.94018Yu, Qiang; Liu, Fawang; Turner, Ian; Burrage, Kevin; Vegh, Viktor 4 2012 Fractional models for the migration of biological cells in complex spatial domains. Zbl 1387.92013Cusimano, Nicole; Burrage, Kevin; Burrage, Pamela 1 2012 Novel techniques in parameter estimation for fractional dynamical models arising from biological systems. Zbl 1228.93114Liu, F.; Burrage, K. 25 2011 Numerical analysis for a variable-order nonlinear cable equation. Zbl 1243.65103Chen, 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 1218.65011Komori, Yoshio; Burrage, Kevin 5 2011 Bayes-optimal chemotaxis. Zbl 1208.92008Mortimer, Duncan; Dayan, Peter; Burrage, Kevin; Goodhill, Geoffrey J. 2 2011 Novel numerical methods for time-space fractional reaction diffusion equations in two dimensions. Zbl 1390.65093Yang, Qianqian; Moroney, Tim; Burrage, Kevin; Turner, Ian; Liu, Fawang 8 2010 Optimizing chemotaxis by measuring unbound-bound transitions. Zbl 1186.92011Mortimer, 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 1211.92017MacNamara, Shev; Burrage, Kevin 2 2010 Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term. Zbl 1170.65107Liu, F.; Yang, C.; Burrage, K. 109 2009 Accurate stationary densities with partitioned numerical methods for stochastic differential equations. Zbl 1197.60068Burrage, Kevin; Lythe, Grant 10 2009 Spectral approximation of time windows in the solution of dissipative linear differential equations. Zbl 1195.65091Burrage, 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 1165.92019MacNamara, Shev; Burrage, Kevin 3 2009 Opportunistic timing and manipulation in Australian federal elections. Zbl 1157.91331Lesmono, Dharma; Tonkes, Elliot; Burrage, Kevin 2 2009 Finite difference methods and a Fourier analysis for the fractional reaction-subdiffusion equation. Zbl 1144.65057Chen, Chang-Ming; Liu, F.; Burrage, K. 83 2008 Multiscale modeling of chemical kinetics via the master equation. Zbl 1153.60370Macnamara, Shev; Burrage, Kevin; Sidje, Roger B. 27 2008 Effects of intrinsic and extrinsic noise can accelerate juxtacrine pattern formation. Zbl 1142.92002Rudge, Tim; Burrage, Kevin 3 2008 Stochastic simulation of chemical reactions in spatially complex media. Zbl 1137.92015Nicolau, Dan V. jun.; Burrage, Kevin 3 2008 Fast generalized cross validation using Krylov subspace methods. Zbl 1157.65012Sidje, Roger B.; Williams, Alan B.; Burrage, Kevin 2 2008 A note on the existence and uniqueness of a bounded mean-reverting prosess. Zbl 1214.60025Lesmono, 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 1193.76093Liu, Fawang; Zhuang, P.; Anh, V.; Turner, I.; Burrage, K. 225 2007 Stochastic delay differential equations for genetic regulatory networks. Zbl 1112.92029Tian, Tianhai; Burrage, Kevin; Burrage, Pamela M.; Carletti, Margherita 52 2007 Numerical methods for second-order stochastic differential equations. Zbl 1144.65004Burrage, Kevin; Lenane, Ian; Lythe, Grant 18 2007 Inexact uniformization method for computing transient distributions of Markov chains. Zbl 1154.65300Sidje, 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 1334.92475MacNamara, Shev F.; Burrage, Kevin; Sidje, Roger B. 2 2007 A note on the balanced method. Zbl 1116.65004Alcock, Jamie; Burrage, Kevin 30 2006 The undirected feedback vertex set problem has a Poly\((k)\) kernel. Zbl 1154.68421Burrage, Kevin; Estivill-Castro, Vladimir; Fellows, Michael; Langston, Michael; Mac, Shev; Rosamond, Frances 19 2006 Accelerated leap methods for simulating discrete stochastic chemical kinetics. Zbl 1132.93345Burrage, Kevin; Mac, Shev; Tian, Tianhai 5 2006 A continuous time model for election timing. Zbl 1183.91044Lesmono, D.; Tonkes, E. J.; Burrage, K. 1 2005 QRT: A QR-based tridiagonalization algorithm for nonsymmetric matrices. Zbl 1081.65040Sidje, Roger B.; Burrage, K. 1 2005 Numerical methods for strong solutions of stochastic differential equations: An overview. Zbl 1048.65004Burrage, K.; Burrage, P. M.; Tian, T. 73 2004 Stochastic approaches for modelling in vivo reactions. Zbl 1087.92035Turner, T. E.; Schnell, S.; Burrage, K. 39 2004 Numerical simulation of stochastic ordinary differential equations in biomathematical modelling. Zbl 1039.65005Carletti, M.; Burrage, K.; Burrage, P. M. 36 2004 Implicit stochastic Runge-Kutta methods for stochastic differential equations. Zbl 1048.65005Burrage, Kevin; Tian, Tianhai 20 2004 Adaptive stepsize based on control theory for stochastic differential equations. Zbl 1049.65009Burrage, P. M.; Herdiana, R.; Burrage, K. 14 2004 A genetic estimation algorithm for parameters of stochastic ordinary differential equations. Zbl 1429.62362Alcock, Jamie; Burrage, Kevin 6 2004 An early political election problem. Zbl 1097.91070Lesmono, D.; Tonkes, E. J.; Burrage, K. 2 2004 Bistability and switching in the lysis/lysogeny genetic regulatory network of bacteriophage \(\lambda\). Zbl 1439.92096Tian, Tianhai; Burrage, Kevin 1 2004 On the convergence of LMF-type methods for SODEs. Zbl 1167.65321Carreras, Giulia; Brugnano, Luigi; Burrage, Kevin 1 2004 Accuracy issues of Monte-Carlo methods for valuing American options. Zbl 1123.91326Tian, Tianhai; Burrage, Kevin 3 2003 Convergence of the parallel chaotic waveform relaxation method for stiff systems. Zbl 1016.65058Yuan, Dongjin; Burrage, Kevin 2 2003 A variable stepsize implementation for stochastic differential equations. Zbl 1034.65003Burrage, P. M.; Burrage, K. 28 2002 Two-stage stochastic Runge-Kutta methods for stochastic differential equations. Zbl 1016.65002Tian, T. H.; Burrage, K. 14 2002 Predictor-corrector methods of Runge-Kutta type for stochastic differential equations. Zbl 1026.60075Burrage, Kevin; Tian, Tianhai 10 2002 A four-stage index 2 diagonally implicit Runge-Kutta method. Zbl 0993.65088Williams, Russell; Burrage, Kevin; Cameron, Ian; Kerr, Minnie 8 2002 New multivalue methods for differential algebraic equations. Zbl 1055.65101Kerr, Minnie; Burrage, Kevin 1 2002 Implicit Taylor methods for stiff stochastic differential equations. Zbl 0983.65007Tian, Tianhai; Burrage, Kevin 37 2001 The composite Euler method for stiff stochastic differential equations. Zbl 0987.65009Burrage, Kevin; Tian, Tianhai 29 2001 Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations. Zbl 0991.65005Burrage, Kevin; Tian, Tianhai 9 2001 Acceleration of convergence of static and dynamic iterations. Zbl 0992.65077Burrage, K.; Hertono, G.; Jackiewicz, Z.; Welfert, B. D. 1 2001 Order conditions of stochastic Runge–Kutta methods by B-series. Zbl 0983.65006Burrage, K.; Burrage, P. M. 61 2000 Numerical solutions of stochastic differential equations – implementation and stability issues. Zbl 0971.65003Burrage, Kevin; Burrage, Pamela; Mitsui, Takemoto 40 2000 A note on the stability properties of the Euler methods for solving stochastic differential equations. Zbl 0980.60083Burrage, Kevin; Tian, Tianhai 17 2000 Adams-type methods for the numerical solution of stochastic ordinary differential equations. Zbl 0963.65004Brugnano, L.; Burrage, K.; Burrage, P. M. 16 2000 Stochastic methods for ill-posed problems. Zbl 0960.65011Burrage, K.; Piskarev, S. 2 2000 Parallel iterated methods based on variable step-size multistep Runge-Kutta methods of Radau type for stiff problems. Zbl 0949.65073Burrage, K.; Suhartanto, H. 1 2000 Parallel half-block methods for initial value problems. Zbl 0952.65055Burrage, Kevin; Tian, Tianhai 1 2000 High strong order methods for non-commutative stochastic ordinary differential equation systems and the Magnus formula. Zbl 1194.65023Burrage, K.; Burrage, P. M. 40 1999 ...and 51 more Documents all cited Publications top 5 cited Publications all top 5 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 ...and 2,459 more Authors all top 5 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 39 Applied Mathematical Modelling 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 21 Abstract and Applied Analysis 21 Fractional Calculus & Applied Analysis 19 Computing 18 Mathematical Problems in Engineering 17 Computer Methods in Applied Mechanics and Engineering 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. 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