A Sylvester-Based IMEXMethod via Differentiation Matrices for Solving Nonlinear Parabolic Equations

作     者：Francisco de la Hoz Fernando Vadillo 

作者机构：Department of Applied MathematicsStatistics and Operations ResearchFaculty of Science and TechnologyUniversity of the Basque Country UPV/EHUBarrio Sarriena S/N48940 LeioaSpain 

出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)

年 卷 期：2013年第14卷第9期

页      面：1001-1026页

核心收录：

学科分类：07[理学] 0704[理学-天文学] 0701[理学-数学] 0702[理学-物理学] 070101[理学-基础数学] 

基　　金：MEC (Spain) [MTM2011-24054] Basque Government [IT-305-07] 

主　　题：Semi-linear diffusion equations pseudo-spectral methods differentiation matrices Hermite functions sinc functions rational Chebyshev polynomials IMEX methods Sylvester equations blow-up 

摘      要：In this paper we describe a new pseudo-spectral method to solve numerically two and three-dimensional nonlinear diffusion equations over unbounded domains,taking Hermite functions,sinc functions,and rational Chebyshev polynomials as basis *** idea is to discretize the equations by means of differentiation matrices and to relate them to Sylvester-type equations by means of a fourth-order implicit-explicit scheme,being of particular interest the treatment of three-dimensional Sylvester equations that we *** resulting method is easy to understand and express,and can be implemented in a transparent way by means of a few lines of *** test numerically the three choices of basis functions,showing the convenience of this new approach,especially when rational Chebyshev polynomials are considered.