A Sylvester-Based IMEX Method via Differentiation Matrices for Solving Nonlinear Parabolic Equations
Year: 2013
Communications in Computational Physics, Vol. 14 (2013), Iss. 4 : pp. 1001–1026
Abstract
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 functions. The 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 make. The resulting method is easy to understand and express, and can be implemented in a transparent way by means of a few lines of code. We test numerically the three choices of basis functions, showing the convenience of this new approach, especially when rational Chebyshev polynomials are considered.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.050612.180113a
Communications in Computational Physics, Vol. 14 (2013), Iss. 4 : pp. 1001–1026
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 26