Edit Profile (opens in new tab) Burrage, Kevin Co-Author Distance Author ID: burrage.kevin Published as: Burrage, Kevin; Burrage, K. Homepage: https://staff.qut.edu.au/staff/kevin.burrage External Links: MGP · ORCID · Google Scholar · dblp Documents Indexed: 190 Publications since 1978, including 1 Book 3 Contributions as Editor Reviewing Activity: 274 Reviews Co-Authors: 136 Co-Authors with 168 Joint Publications 2,889 Co-Co-Authors all top 5 Co-Authors 24 single-authored 27 Liu, Fawang 24 Burrage, Pamela M. 23 Turner, Ian William 15 Tian, Tianhai 9 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 Butcher, John C. 3 Chen, Changming 3 Lawson, Brodie A. J. 3 Suhartanto, Heru 3 Tonkes, E. J. 3 Weber Dos Santos, Rodrigo 3 Yang, Guoguo 2 Altas, Irfan 2 Brugnano, Luigi 2 Carletti, Margherita 2 Chen, Jinghua 2 Chen, Luonan 2 Cusimano, Nicole 2 Dayan, Peter 2 Ding, Xiaohua 2 Donovan, Diane M. 2 Feng, Libo 2 Goodhill, Geoffrey J. 2 Herdiana, R. 2 Hundsdorfer, Willem H. 2 Karniadakis, George Em 2 Kerr, Minnie 2 Mac, Shev 2 Mortimer, Duncan 2 Perré, Patrick 2 Piskarëv, S. I. 2 Renaut, Rosemary Anne 2 Simpson, Matthew J. 2 Somathilake, Lekam Watte 2 Walmsley, John L. 2 Yang, Qianqian 2 Yazıcı, Emine Şule 2 Zhang, Chengjian 1 Abdullah, Farah Aini 1 Ahn, Vo 1 Baker, Christopher Thomas Hale 1 Berg, Lucas A. 1 Browning, Alexander P. 1 Cameron, Ian T. 1 Cardone, Angelamaria 1 Carreras, Giulia 1 Cavenagh, Nicholas J. 1 Chan, Robert Peng Kong 1 Chen, Phoebe 1 Chen, Shiping 1 Christen, Peter 1 D’Ambrosio, Raffaele 1 Dangerfield, Ciara E. 1 Duc, K. Dao 1 Dyke, Carolyn 1 Eldershaw, Craig 1 Eremin, Alexey S. 1 Estivill-Castro, Vladimir 1 Farquhar, Megan E. 1 Fellows, Michael Ralph 1 Fine, J. M. 1 Guo, Ling 1 Hale, Nicholas 1 Hamilton, Nicholas A. 1 Hanan, James 1 Hegland, Markus 1 Hertono, G. 1 Holcman, David 1 Jiang, Xiaoyun 1 Langston, Michael A. 1 Leier, André 1 Lenane, Ian 1 Li, Changpin 1 Li, Tianzeng 1 Liu, Qingxia 1 Mapder, Tarunendu 1 Marquez-Lago, Tatiana T. 1 Mayer, D. G. 1 McCourt, Thomas A. 1 McLean, William 1 Mirams, Gary R. ...and 36 more Co-Authors all top 5 Serials 17 Journal of Computational and Applied Mathematics 14 BIT 13 SIAM Journal on Numerical Analysis 13 Applied Numerical Mathematics 13 The ANZIAM Journal 9 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 SIAM Journal on Matrix Analysis and Applications 2 Multiscale Modeling & Simulation 1 Bulletin of the Australian Mathematical Society 1 Computer Physics Communications 1 Discrete Mathematics 1 Journal of Mathematical Analysis and Applications 1 Journal of Mathematical Biology 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Bulletin of Mathematical Biology 1 Computing 1 The Fibonacci Quarterly 1 Mathematics and Computers in Simulation 1 Numerical Functional Analysis and Optimization 1 Journal of Computational Mathematics 1 Parallel Computing 1 Numerical Methods for Partial Differential Equations 1 Journal of Scientific Computing 1 Annals of Operations Research 1 Neural Computation 1 European Journal of Operational Research 1 Linear Algebra and its Applications 1 Computational Statistics and Data Analysis 1 New Zealand Journal of Mathematics 1 Numerical Linear Algebra with Applications 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Journal of Applied Mathematics and Computing 1 Computational Biology and Chemistry 1 Journal of the Indonesian Mathematical Society 1 Mediterranean Journal of Mathematics 1 JNAIAM. Journal of Numerical Analysis, Industrial and Applied Mathematics 1 Journal of Fractional Calculus and Applications 1 Axioms 1 Stochastic and Partial Differential Equations. Analysis and Computations 1 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Cogent Mathematics & Statistics all top 5 Fields 150 Numerical analysis (65-XX) 65 Ordinary differential equations (34-XX) 53 Probability theory and stochastic processes (60-XX) 37 Partial differential equations (35-XX) 34 Biology and other natural sciences (92-XX) 12 Real functions (26-XX) 9 Fluid mechanics (76-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Statistics (62-XX) 4 Computer science (68-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 General and overarching topics; collections (00-XX) 3 Integral equations (45-XX) 3 Mechanics of deformable solids (74-XX) 3 Operations research, mathematical programming (90-XX) 2 History and biography (01-XX) 2 Special functions (33-XX) 2 Operator theory (47-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Systems theory; control (93-XX) 1 Combinatorics (05-XX) 1 Number theory (11-XX) 1 Approximations and expansions (41-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Geophysics (86-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 160 Publications have been cited 4,104 times in 2,649 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. 290 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. 205 2014 Fourier spectral methods for fractional-in-space reaction-diffusion equations. Zbl 1306.65265Bueno-Orovio, Alfonso; Kay, David; Burrage, Kevin 175 2014 Stability criteria for implicit Runge-Kutta methods. Zbl 0396.65043Burrage, Kevin; Butcher, J. C. 133 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. 129 2009 An efficient implicit FEM scheme for fractional-in-space reaction-diffusion equations. Zbl 1253.65146Burrage, Kevin; Hale, Nicholas; Kay, David 122 2012 Numerical methods and analysis for a class of fractional advection-dispersion models. Zbl 1268.65124Liu, F.; Zhuang, P.; Burrage, K. 116 2012 Non-linear stability of a general class of differential equation methods. Zbl 0431.65051Burrage, Kevin; Butcher, J. C. 115 1980 Parallel and sequential methods for ordinary differential equations. Zbl 0838.65073Burrage, Kevin 113 1995 A new fractional finite volume method for solving the fractional diffusion equation. Zbl 1429.65213Liu, F.; Zhuang, P.; Turner, I.; Burrage, K.; Anh, V. 110 2014 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. 97 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. 94 2012 Finite difference methods and a Fourier analysis for the fractional reaction-subdiffusion equation. Zbl 1144.65057Chen, Chang-Ming; Liu, F.; Burrage, K. 93 2008 High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations. Zbl 0868.65101Burrage, K.; Burrage, P. M. 88 1996 Numerical methods for strong solutions of stochastic differential equations: An overview. Zbl 1048.65004Burrage, K.; Burrage, P. M.; Tian, T. 78 2004 A special family of Runge-Kutta methods for solving stiff differential equations. Zbl 0384.65034Burrage, Kevin 74 1978 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. 72 2015 Order conditions of stochastic Runge–Kutta methods by B-series. Zbl 0983.65006Burrage, K.; Burrage, P. M. 71 2000 An implementation of singly-implicit Runge-Kutta methods. Zbl 0456.65040Burrage, K.; Butcher, J. C.; Chipman, F. H. 66 1980 Restarted GMRES preconditioned by deflation. Zbl 0854.65025Erhel, Jocelyne; Burrage, Kevin; Pohl, Bert 60 1996 Stochastic delay differential equations for genetic regulatory networks. Zbl 1112.92029Tian, Tianhai; Burrage, Kevin; Burrage, Pamela M.; Carletti, Margherita 55 2007 Novel techniques in parameter estimation for fractional dynamical models arising from biological systems. Zbl 1228.93114Liu, F.; Burrage, K. 52 2011 Implicit Taylor methods for stiff stochastic differential equations. Zbl 0983.65007Tian, Tianhai; Burrage, Kevin 48 2001 A stable fast time-stepping method for fractional integral and derivative operators. Zbl 1406.65047Zeng, Fanhai; Turner, Ian; Burrage, Kevin 47 2018 Numerical solutions of stochastic differential equations – implementation and stability issues. Zbl 0971.65003Burrage, Kevin; Burrage, Pamela; Mitsui, Takemoto 45 2000 High strong order methods for non-commutative stochastic ordinary differential equation systems and the Magnus formula. Zbl 1194.65023Burrage, K.; Burrage, P. M. 44 1999 Stochastic approaches for modelling in vivo reactions. Zbl 1087.92035Turner, T. E.; Schnell, S.; Burrage, K. 41 2004 Numerical simulation of stochastic ordinary differential equations in biomathematical modelling. Zbl 1039.65005Carletti, M.; Burrage, K.; Burrage, P. M. 40 2004 A study of B-convergence of Runge-Kutta methods. Zbl 0572.65053Burrage, K.; Hundsdorfer, W. H.; Verwer, J. G. 39 1986 The composite Euler method for stiff stochastic differential equations. Zbl 0987.65009Burrage, Kevin; Tian, Tianhai 37 2001 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 36 2016 A variable stepsize implementation for stochastic differential equations. Zbl 1034.65003Burrage, P. M.; Burrage, K. 35 2002 A note on the balanced method. Zbl 1116.65004Alcock, Jamie; Burrage, Kevin 35 2006 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. 35 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. 33 2012 Low rank Runge-Kutta methods, symplecticity and stochastic Hamiltonian problems with additive noise. Zbl 1245.65007Burrage, Kevin; Burrage, Pamela M. 33 2012 Numerical methods for second-order stochastic differential equations. Zbl 1144.65004Burrage, Kevin; Lenane, Ian; Lythe, Grant 31 2007 Multiscale modeling of chemical kinetics via the master equation. Zbl 1153.60370Macnamara, Shev; Burrage, Kevin; Sidje, Roger B. 30 2008 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. 28 1990 Numerical solution of time fractional diffusion systems. Zbl 1372.65228Burrage, Kevin; Cardone, Angelamaria; D’Ambrosio, Raffaele; Paternoster, Beatrice 27 2017 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 27 2006 Structure-preserving Runge-Kutta methods for stochastic Hamiltonian equations with additive noise. Zbl 1291.65017Burrage, Pamela M.; Burrage, Kevin 25 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. 25 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 24 2013 On the performance of various adaptive preconditioned GMRES strategies. Zbl 0937.65036Burrage, K.; Erhel, J. 24 1998 Parallel methods for initial value problems. Zbl 0781.65060Burrage, Kevin 23 1993 Efficient block predictor-corrector methods with a small number of corrections. Zbl 0782.65088Burrage, Kevin 22 1993 Implicit stochastic Runge-Kutta methods for stochastic differential equations. Zbl 1048.65005Burrage, Kevin; Tian, Tianhai 22 2004 Efficiently implementable algebraically stable Runge-Kutta methods. Zbl 0483.65040Burrage, Kevin 21 1982 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. 21 2014 Runge-Kutta methods for stochastic differential equations. Zbl 0824.65148Burrage, K.; Platen, E. 20 1994 Numerical analysis for a variable-order nonlinear cable equation. Zbl 1243.65103Chen, Chang-Ming; Liu, F.; Burrage, K. 20 2011 Inexact uniformization method for computing transient distributions of Markov chains. Zbl 1154.65300Sidje, Roger B.; Burrage, Kevin; Macnamara, Shev 19 2007 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 Two-stage stochastic Runge-Kutta methods for stochastic differential equations. Zbl 1016.65002Tian, T. H.; Burrage, K. 18 2002 Order properties of implicit multivalue methods for ordinary differential equations. Zbl 0637.65066Burrage, Kevin 18 1988 High order algebraically stable multistep Runge-Kutta methods. Zbl 0611.65046Burrage, K. 18 1987 Adams-type methods for the numerical solution of stochastic ordinary differential equations. Zbl 0963.65004Brugnano, L.; Burrage, K.; Burrage, P. M. 18 2000 A note on the stability properties of the Euler methods for solving stochastic differential equations. Zbl 0980.60083Burrage, Kevin; Tian, Tianhai 17 2000 An investigation of nonlinear time-fractional anomalous diffusion models for simulating transport processes in heterogeneous binary media. Zbl 1452.76227Feng, Libo; Turner, Ian; Perré, Patrick; Burrage, Kevin 17 2021 Efficient multistep methods for tempered fractional calculus: algorithms and simulations. Zbl 07099350Guo, Ling; Zeng, Fanhai; Turner, Ian; Burrage, Kevin; Karniadakis, George Em 17 2019 A Jacobi waveform relaxation method for ODEs. Zbl 0923.65045Sand, J.; Burrage, K. 16 1999 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 16 2018 Adaptive stepsize based on control theory for stochastic differential equations. Zbl 1049.65009Burrage, P. M.; Herdiana, R.; Burrage, K. 15 2004 A stochastic exponential Euler scheme for simulation of stiff biochemical reaction systems. Zbl 1307.65011Komori, Yoshio; Burrage, Kevin 15 2014 A numerical method for the fractional FitzHugh-Nagumo monodomain model. Zbl 1390.65074Liu, Fawang; Turner, Ian; Ahn, Vo; Yang, Qianqian; Burrage, Kevin 14 2012 A high accuracy defect-correction multigrid method for the steady incompressible Navier-Stokes equations. Zbl 0811.65113Altas, Irfan; Burrage, Kevin 14 1994 Numerical simulation of the fractional Bloch equations. Zbl 1291.65224Yu, Q.; Liu, F.; Turner, I.; Burrage, K. 14 2014 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. 14 2013 Some novel techniques of parameter estimation for dynamical models in biological systems. Zbl 1402.92203Liu, F.; Burrage, K.; Hamilton, N. A. 14 2013 Strong first order \(S\)-ROCK methods for stochastic differential equations. Zbl 1258.65007Komori, Yoshio; Burrage, Kevin 14 2013 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. 13 2017 Accurate stationary densities with partitioned numerical methods for stochastic differential equations. Zbl 1197.60068Burrage, Kevin; Lythe, Grant 13 2009 A boundary preserving numerical algorithm for the Wright-Fisher model with mutation. Zbl 1255.65019Dangerfield, C. E.; Kay, D.; MacNamara, S.; Burrage, K. 13 2012 The order of B-convergence of algebraically stable Runge-Kutta methods. Zbl 0629.65075Burrage, K.; Hundsdorfer, W. H. 13 1987 High order algebraically stable Runge-Kutta methods. Zbl 0401.65049Burrage, Kevin 13 1978 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 12 2010 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. 12 1997 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 11 2012 Order results for mono-implicit Runge-Kutta methods. Zbl 0809.65080Burrage, K.; Chipman, F. H.; Muir, P. H. 11 1994 Predictor-corrector methods of Runge-Kutta type for stochastic differential equations. Zbl 1026.60075Burrage, Kevin; Tian, Tianhai 11 2002 Preconditioning waveform relaxation iterations for differential systems. Zbl 0864.65049Burrage, K.; Jackiewicz, Z.; Nørsett, S. P.; Renaut, R. A. 11 1996 Weak second order S-ROCK methods for Stratonovich stochastic differential equations. Zbl 1238.60063Komori, Yoshio; Burrage, Kevin 11 2012 Weak second order explicit exponential Runge-Kutta methods for stochastic differential equations. Zbl 1387.65064Komori, Yoshio; Cohen, David; Burrage, Kevin 11 2017 The error behaviour of a general class of predictor-corrector methods. Zbl 0743.65064Burrage, Kevin 10 1991 The search for the Holy Grail, or: Predictor-corrector methods for solving ODEIVPs. Zbl 0787.65048Burrage, Kevin 10 1993 Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations. Zbl 0991.65005Burrage, Kevin; Tian, Tianhai 10 2001 A four-stage index 2 diagonally implicit Runge-Kutta method. Zbl 0993.65088Williams, Russell; Burrage, Kevin; Cameron, Ian; Kerr, Minnie 10 2002 Parallel iterated methods based on multistep Runge-Kutta methods of Radau type. Zbl 0884.65080Burrage, K.; Suhartanto, H. 10 1997 Parallel methods for ODEs. Zbl 0900.65210Burrage, Kevin 10 1997 On the performance of parallel waveform relaxations for differential systems. Zbl 0855.65074Burrage, Kevin; Dyke, Carolyn; Pohl, Bert 10 1996 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 9 2017 A deflation technique for linear systems of equations. Zbl 0914.65025Burrage, K.; Erhel, J.; Pohl, B.; Williams, A. 9 1998 Simplifying assumptions for the order of partitioned multivalue methods. Zbl 0477.65051Burrage, Kevin; Moss, Pamela 9 1980 Strong predictor-corrector approximation for stochastic delay differential equations. Zbl 1349.65034Niu, Yuanling; Zhang, Chengjian; Burrage, Kevin 8 2015 On order reduction for Runge-Kutta methods applied to differential/algebraic systems and to stiff systems of ODEs. Zbl 0708.65069Burrage, Kevin; Petzold, Linda 8 1990 Stable strong order 1.0 schemes for solving stochastic ordinary differential equations. Zbl 1259.65002Alcock, Jamie; Burrage, Kevin 8 2012 Bistability and switching in the lysis/lysogeny genetic regulatory network of bacteriophage \(\lambda\). Zbl 1439.92096Tian, Tianhai; Burrage, Kevin 7 2004 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 The use of a time-fractional transport model for performing computational homogenisation of 2D heterogeneous media exhibiting memory effects. Zbl 07662519Feng, Libo; Turner, Ian; Perré, Patrick; Burrage, Kevin 2 2023 Graph-based homogenisation for modelling cardiac fibrosis. Zbl 07525124Farquhar, 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 1452.76227Feng, Libo; Turner, Ian; Perré, Patrick; Burrage, Kevin 17 2021 A class of new Magnus-type methods for semi-linear non-commutative Itô stochastic differential equations. Zbl 1482.65013Yang, Guoguo; Burrage, Kevin; Komori, Yoshio; Burrage, Pamela; Ding, Xiaohua 4 2021 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. 4 2020 Efficient multistep methods for tempered fractional calculus: algorithms and simulations. Zbl 07099350Guo, Ling; Zeng, Fanhai; Turner, Ian; Burrage, Kevin; Karniadakis, George Em 17 2019 S-ROCK methods for stochastic delay differential equations with one fixed delay. Zbl 1417.65023Komori, Yoshio; Eremin, Alexey; Burrage, Kevin 4 2019 A discrete least squares collocation method for two-dimensional nonlinear time-dependent partial differential equations. Zbl 1452.65284Zeng, Fanhai; Turner, Ian; Burrage, Kevin; Wright, Stephen J. 2 2019 Wider contours and adaptive contours. Zbl 07075714MacNamara, Shev; McLean, William; Burrage, Kevin 1 2019 Optimal control of acute myeloid leukaemia. Zbl 1411.92149Sharp, Jesse A.; Browning, Alexander P.; Mapder, Tarunendu; Burrage, Kevin; Simpson, Matthew J. 1 2019 A stable fast time-stepping method for fractional integral and derivative operators. Zbl 1406.65047Zeng, Fanhai; Turner, Ian; Burrage, Kevin 47 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 16 2018 A space-fractional-reaction-diffusion model for pattern formation in coral reefs. Zbl 1426.92007Somathilake, Lekam Watte; Burrage, Kevin 6 2018 Estimates of the coverage of parameter space by Latin hypercube and orthogonal array-based sampling. Zbl 1480.62158Donovan, D.; Burrage, Kevin; Burrage, Pamela; McCourt, T. A.; Thompson, B.; Yazici, E. Ş. 3 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. 3 2018 Numerical solution of time fractional diffusion systems. Zbl 1372.65228Burrage, Kevin; Cardone, Angelamaria; D’Ambrosio, Raffaele; Paternoster, Beatrice 27 2017 Numerical solution of the time fractional reaction-diffusion equation with a moving boundary. Zbl 1415.65205Zheng, Minling; Liu, Fawang; Liu, Qingxia; Burrage, Kevin; Simpson, Matthew J. 13 2017 Weak second order explicit exponential Runge-Kutta methods for stochastic differential equations. Zbl 1387.65064Komori, Yoshio; Cohen, David; Burrage, Kevin 11 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 9 2017 Exact solutions to the fractional time-space Bloch-Torrey equation for magnetic resonance imaging. Zbl 1510.92110Bueno-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 1382.65290Chen, Shiping; Liu, Fawang; Jiang, X.; Turner, Ian; Burrage, Kevin 36 2016 Modelling biochemical reaction systems by stochastic differential equations with reflection. Zbl 1343.92165Niu, 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 1349.65316Liu, Fawang; Zhuang, P.; Turner, I.; Anh, V.; Burrage, K. 72 2015 Strong predictor-corrector approximation for stochastic delay differential equations. Zbl 1349.65034Niu, Yuanling; Zhang, Chengjian; Burrage, Kevin 8 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 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 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. 205 2014 Fourier spectral methods for fractional-in-space reaction-diffusion equations. Zbl 1306.65265Bueno-Orovio, Alfonso; Kay, David; Burrage, Kevin 175 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. 110 2014 Structure-preserving Runge-Kutta methods for stochastic Hamiltonian equations with additive noise. Zbl 1291.65017Burrage, Pamela M.; Burrage, Kevin 25 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. 25 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. 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 A stochastic exponential Euler scheme for simulation of stiff biochemical reaction systems. Zbl 1307.65011Komori, Yoshio; Burrage, Kevin 15 2014 Numerical simulation of the fractional Bloch equations. Zbl 1291.65224Yu, Q.; Liu, F.; Turner, I.; Burrage, K. 14 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 24 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. 14 2013 Some novel techniques of parameter estimation for dynamical models in biological systems. Zbl 1402.92203Liu, F.; Burrage, K.; Hamilton, N. A. 14 2013 Strong first order \(S\)-ROCK methods for stochastic differential equations. Zbl 1258.65007Komori, Yoshio; Burrage, Kevin 14 2013 A derivative-free explicit method with order 1.0 for solving stochastic delay differential equations. Zbl 1288.65010Niu, Yuanling; Burrage, Kevin; Zhang, Chengjian 4 2013 Numerical techniques for simulating a fractional mathematical model of epidermal wound healing. Zbl 1325.92043Chen, J.; Liu, F.; Burrage, K.; Shen, S. 3 2013 An efficient implicit FEM scheme for fractional-in-space reaction-diffusion equations. Zbl 1253.65146Burrage, Kevin; Hale, Nicholas; Kay, David 122 2012 Numerical methods and analysis for a class of fractional advection-dispersion models. Zbl 1268.65124Liu, F.; Zhuang, P.; Burrage, K. 116 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. 97 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. 94 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. 33 2012 Low rank Runge-Kutta methods, symplecticity and stochastic Hamiltonian problems with additive noise. Zbl 1245.65007Burrage, Kevin; Burrage, Pamela M. 33 2012 A numerical method for the fractional FitzHugh-Nagumo monodomain model. Zbl 1390.65074Liu, Fawang; Turner, Ian; Ahn, Vo; Yang, Qianqian; Burrage, Kevin 14 2012 A boundary preserving numerical algorithm for the Wright-Fisher model with mutation. Zbl 1255.65019Dangerfield, C. E.; Kay, D.; MacNamara, S.; Burrage, K. 13 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 11 2012 Weak second order S-ROCK methods for Stratonovich stochastic differential equations. Zbl 1238.60063Komori, Yoshio; Burrage, Kevin 11 2012 Stable strong order 1.0 schemes for solving stochastic ordinary differential equations. Zbl 1259.65002Alcock, Jamie; Burrage, Kevin 8 2012 Fractional models for the migration of biological cells in complex spatial domains. Zbl 1387.92013Cusimano, Nicole; Burrage, Kevin; Burrage, Pamela 2 2012 Novel techniques in parameter estimation for fractional dynamical models arising from biological systems. Zbl 1228.93114Liu, F.; Burrage, K. 52 2011 Numerical analysis for a variable-order nonlinear cable equation. Zbl 1243.65103Chen, 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 1218.65011Komori, 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 12 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. 129 2009 Accurate stationary densities with partitioned numerical methods for stochastic differential equations. Zbl 1197.60068Burrage, Kevin; Lythe, Grant 13 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. 93 2008 Multiscale modeling of chemical kinetics via the master equation. Zbl 1153.60370Macnamara, Shev; Burrage, Kevin; Sidje, Roger B. 30 2008 Stochastic simulation of chemical reactions in spatially complex media. Zbl 1137.92015Nicolau, Dan V. jun.; Burrage, Kevin 4 2008 Fast generalized cross validation using Krylov subspace methods. Zbl 1157.65012Sidje, Roger B.; Williams, Alan B.; Burrage, Kevin 3 2008 Effects of intrinsic and extrinsic noise can accelerate juxtacrine pattern formation. Zbl 1142.92002Rudge, Tim; Burrage, Kevin 3 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. 290 2007 Stochastic delay differential equations for genetic regulatory networks. Zbl 1112.92029Tian, Tianhai; Burrage, Kevin; Burrage, Pamela M.; Carletti, Margherita 55 2007 Numerical methods for second-order stochastic differential equations. Zbl 1144.65004Burrage, Kevin; Lenane, Ian; Lythe, Grant 31 2007 Inexact uniformization method for computing transient distributions of Markov chains. Zbl 1154.65300Sidje, Roger B.; Burrage, Kevin; Macnamara, Shev 19 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 35 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 27 2006 Accelerated leap methods for simulating discrete stochastic chemical kinetics. Zbl 1132.93345Burrage, Kevin; Mac, Shev; Tian, Tianhai 3 2006 QRT: A QR-based tridiagonalization algorithm for nonsymmetric matrices. Zbl 1081.65040Sidje, Roger B.; Burrage, K. 2 2005 A continuous time model for election timing. Zbl 1183.91044Lesmono, D.; Tonkes, E. J.; Burrage, K. 1 2005 Numerical methods for strong solutions of stochastic differential equations: An overview. Zbl 1048.65004Burrage, K.; Burrage, P. M.; Tian, T. 78 2004 Stochastic approaches for modelling in vivo reactions. Zbl 1087.92035Turner, T. E.; Schnell, S.; Burrage, K. 41 2004 Numerical simulation of stochastic ordinary differential equations in biomathematical modelling. Zbl 1039.65005Carletti, M.; Burrage, K.; Burrage, P. M. 40 2004 Implicit stochastic Runge-Kutta methods for stochastic differential equations. Zbl 1048.65005Burrage, Kevin; Tian, Tianhai 22 2004 Adaptive stepsize based on control theory for stochastic differential equations. Zbl 1049.65009Burrage, P. M.; Herdiana, R.; Burrage, K. 15 2004 Bistability and switching in the lysis/lysogeny genetic regulatory network of bacteriophage \(\lambda\). Zbl 1439.92096Tian, Tianhai; Burrage, Kevin 7 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 On the convergence of LMF-type methods for SODEs. Zbl 1167.65321Carreras, Giulia; Brugnano, Luigi; Burrage, Kevin 1 2004 Convergence of the parallel chaotic waveform relaxation method for stiff systems. Zbl 1016.65058Yuan, Dongjin; Burrage, Kevin 2 2003 Accuracy issues of Monte-Carlo methods for valuing American options. Zbl 1123.91326Tian, Tianhai; Burrage, Kevin 2 2003 A variable stepsize implementation for stochastic differential equations. Zbl 1034.65003Burrage, P. M.; Burrage, K. 35 2002 Two-stage stochastic Runge-Kutta methods for stochastic differential equations. Zbl 1016.65002Tian, T. H.; Burrage, K. 18 2002 Predictor-corrector methods of Runge-Kutta type for stochastic differential equations. Zbl 1026.60075Burrage, Kevin; Tian, Tianhai 11 2002 A four-stage index 2 diagonally implicit Runge-Kutta method. Zbl 0993.65088Williams, Russell; Burrage, Kevin; Cameron, Ian; Kerr, Minnie 10 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 48 2001 The composite Euler method for stiff stochastic differential equations. Zbl 0987.65009Burrage, Kevin; Tian, Tianhai 37 2001 ...and 60 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 3,161 Authors 131 Liu, Fawang 89 Burrage, Kevin 76 Turner, Ian William 51 Anh, Vo V. 39 Jiang, Xiaoyun 31 D’Ambrosio, Raffaele 31 Dehghan Takht Fooladi, Mehdi 30 Li, Hong 30 Liu, Yang 29 Abbaszadeh, Mostafa 29 Wang, Hong 27 Huang, Chengming 26 Owolabi, Kolade Matthew 25 Butcher, John C. 25 Feng, Libo 24 Paternoster, Beatrice 24 Zeng, Fanhai 22 Jackiewicz, Zdzislaw 22 Zaky, Mahmoud A. 22 Zhang, Chengjian 21 Gan, Siqing 20 Rößler, Andreas 20 Tang, Yifa 19 Zhang, Hui 18 Karniadakis, George Em 17 Burrage, Pamela M. 17 Cong, Nguyen Huu 17 Hendy, Ahmed S. 17 Sun, Zhizhong 17 Xiao, Aiguo 16 Bhrawy, Ali Hassan 16 Jiang, Daqing 15 Băleanu, Dumitru I. 15 Cao, Wanrong 15 Ding, Xiaohua 15 Li, Xiaoli 14 Brugnano, Luigi 14 Conte, Dajana 14 Fu, Hongfei 14 Hosseini, Seyed Mohammad 14 Li, Changpin 14 Sun, Haiwei 14 Weiner, Rüdiger 14 Zhuang, Pinghui 13 Chen, Changming 13 Komori, Yoshio 13 Li, Shoufu 13 Lu, Shujuan 13 Wang, Yuanming 13 Zheng, Xiangcheng 12 Debrabant, Kristian 12 Ma, Qiang 12 Macías-Díaz, Jorge Eduardo 12 Mohebbi, Akbar 12 van der Houwen, Pieter J. 12 Wen, Liping 12 Xu, Da 11 Atangana, Abdon 11 Bu, Weiping 11 Cardone, Angelamaria 11 González-Pinto, Severiano 11 Huang, Ting-Zhu 11 Khaliq, Abdul Q. M. 11 Kvaerno, Anne 11 Liu, Zhengguang 11 Mao, Xuerong 11 Sidje, Roger B. 11 Spijker, Marc N. 11 Sun, Hongguang 11 Wang, Wansheng 11 Yang, Qianqian 11 Yin, Baoli 11 Zhao, Yanmin 10 Avazzadeh, Zakieh 10 Chen, Shanzhen 10 Gu, Xian-Ming 10 Hairer, Ernst 10 Zheng, Liancun 9 Ding, Hengfei 9 Fan, Zhencheng 9 Heydari, Mohammad Hossien 9 Hong, Jialin 9 Hundsdorfer, Willem H. 9 Liu, Qun 9 Machado, José António Tenreiro 9 Mei, Liquan 9 Nie, Yufeng 9 Rui, Hongxing 9 Wang, Jinfeng 9 Wei, LeiLei 9 Zhang, Haixiang 9 Zhao, Yongliang 8 Deng, Weihua 8 Doha, Eid H. 8 Huang, Jianfei 8 Jiang, Yaolin 8 Jimenez, Juan Carlos 8 Li, Gongsheng 8 Li, Zhiyuan 8 Liu, Huan ...and 3,061 more Authors all top 5 Cited in 312 Serials 236 Journal of Computational and Applied Mathematics 205 Applied Numerical Mathematics 171 Computers & Mathematics with Applications 154 Applied Mathematics and Computation 113 Journal of Computational Physics 112 Numerical Algorithms 102 BIT 91 International Journal of Computer Mathematics 52 Journal of Scientific Computing 44 Mathematics and Computers in Simulation 44 Communications in Nonlinear Science and Numerical Simulation 43 Applied Mathematical Modelling 40 Advances in Difference Equations 39 Computational and Applied Mathematics 37 SIAM Journal on Scientific Computing 35 Numerische Mathematik 33 Chaos, Solitons and Fractals 30 Fractional Calculus & Applied Analysis 29 Applied Mathematics Letters 25 Computer Methods in Applied Mechanics and Engineering 22 SIAM Journal on Numerical Analysis 21 Mathematical Biosciences 21 Abstract and Applied Analysis 20 Journal of Applied Mathematics and Computing 19 Physica A 19 Computing 19 Engineering Analysis with Boundary Elements 19 Mathematical Problems in Engineering 17 Mathematics of Computation 15 Advances in Computational Mathematics 13 Mathematical Methods in the Applied Sciences 13 Communications on Applied Mathematics and Computation 12 Advances in Mathematical Physics 11 Bulletin of Mathematical Biology 11 Stochastic Analysis and Applications 11 Nonlinear Dynamics 10 Calcolo 10 Numerical Methods for Partial Differential Equations 10 Journal of Mathematical Chemistry 10 Advances in Applied Mathematics and Mechanics 10 International Journal of Applied and Computational Mathematics 9 Computers and Fluids 9 International Journal for Numerical Methods in Engineering 9 Fractals 9 Discrete and Continuous Dynamical Systems. 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