MAINI P K, PAINTER K J, NGUYEN PHONG CHAU H. Spatial Pattern Formation in Chemical and Biological Systems[J]. Journal of the Chemical Society, Faraday Transactions, 1997, 93(20): 3601-3610. doi: 10.1039/a702602a
|
BORCKMANS P, DEWEL G, DE WIT A, et al. Diffusive Instabilities and Chemical Reactions[J]. International Journal of Bifurcation and Chaos, 2002, 12(11): 2307-2332. doi: 10.1142/S0218127402005881
|
MERZHANOV A G, RUMANOV E N. Physics of Reaction Waves[J]. Reviews of Modern Physics, 1999, 71(4): 1173-1211. doi: 10.1103/RevModPhys.71.1173
|
HAGAN P S. Spiral Waves in Reaction-Diffusion Equations[J]. SIAM Journal on Applied Mathematics, 1982, 42(4): 762-786. doi: 10.1137/0142054
|
NISHIURA Y, UEYAMA D. Spatio-Temporal Chaos for the Gray-Scott Model[J]. Physica D: Nonlinear Phenomena, 2001, 150(3/4): 137-162.
|
ASCHER U M, RUUTH S J, WETTON B T R. Implicit-Explicit Methods for Time-Dependent Partial Differential Equations[J]. SIAM Journal on Numerical Analysis, 1995, 32(3): 797-823. doi: 10.1137/0732037
|
ASCHER U M, RUUTH S J, SPITERI R J. Implicit-Explicit Runge-Kutta Methods for Time-Dependent Partial Differential Equations[J]. Applied Numerical Mathematics, 1997, 25(2/3): 151-167.
|
CALVO M P, DE FRUTOS J, NOVO J. Linearly Implicit Runge-Kutta Methods for Advection-Reaction-Diffusion Equations[J]. Applied Numerical Mathematics, 2001, 37(4): 535-549. doi: 10.1016/S0168-9274(00)00061-1
|
COX S M, MATTHEWS P C. Exponential Time Differencing for Stiff Systems[J]. Journal of Computational Physics, 2002, 176(2): 430-455. doi: 10.1006/jcph.2002.6995
|
DRISCOLL T A. A Composite Runge-Kutta Method for the Spectral Solution of Semilinear PDEs[J]. Journal of Computational Physics, 2002, 182(2): 357-367. doi: 10.1006/jcph.2002.7127
|
HOCHBRUCK M, LUBICH C, SELHOFER H. Exponential Integrators for Large Systems of Differential Equations[J]. SIAM Journal on Scientific Computing, 1998, 19(5): 1552-1574. doi: 10.1137/S1064827595295337
|
ARRARÁS A, IN'T HOUT K J, HUNDSDORFER W, et al. Modified Douglas Splitting Methods for Reaction-Diffusion Equations[J]. BIT Numerical Mathematics, 2017, 57(2): 261-285. doi: 10.1007/s10543-016-0634-9
|
ARRARÁS A, GASPAR F J, PORTERO L, et al. Domain Decomposition Multigrid Methods for Nonlinear Reaction-Diffusion Problems[J]. Communications in Nonlinear Science and Numerical Simulation, 2015, 20(3): 699-710. doi: 10.1016/j.cnsns.2014.06.044
|
ARRARÁS A, PORTERO L. Improved Accuracy for Time-Splitting Methods for the Numerical Solution of Parabolic Equations[J]. Applied Mathematics and Computation, 2015, 267: 294-303. doi: 10.1016/j.amc.2015.03.073
|
CHEN H, WANG Y. Modified Douglas Splitting Method for Differential Matrix Equations[J]. Journal of Computational and Applied Mathematics, 2021, 384: 113162. doi: 10.1016/j.cam.2020.113162
|
HUNDSDORFER W. Accuracy and Stability of Splitting with Stabilizing Corrections[J]. Applied Numerical Mathematics, 2002, 42(1/3): 213-233.
|
HUNDSDORFER W, VERWER J. Advection-Diffusion Discretizations[M]//Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations. Berlin: Springer, 2003: 215-323.
|
ZHU J F, ZHANG Y T, NEWMAN S A, et al. Application of Discontinuous Galerkin Methods for Reaction-Diffusion Systems in Developmental Biology[J]. Journal of Scientific Computing, 2009, 40(1/3): 391-418.
|