Volume 14, Issue 4
A Sylvester-Based IMEX Method Via Differentiation Matrices for Solving Nonlinear Parabolic Equations

Francisco de la Hoz & Fernando Vadillo

Commun. Comput. Phys., 14 (2013), pp. 1001-1026.

Published online: 2013-10

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  • 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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@Article{CiCP-14-1001, author = {}, title = {A Sylvester-Based IMEX Method Via Differentiation Matrices for Solving Nonlinear Parabolic Equations}, journal = {Communications in Computational Physics}, year = {2013}, volume = {14}, number = {4}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.050612.180113a}, url = {http://global-sci.org/intro/article_detail/cicp/7190.html} }
TY - JOUR T1 - A Sylvester-Based IMEX Method Via Differentiation Matrices for Solving Nonlinear Parabolic Equations JO - Communications in Computational Physics VL - 4 SP - 1001 EP - 1026 PY - 2013 DA - 2013/10 SN - 14 DO - http://dor.org/10.4208/cicp.050612.180113a UR - https://global-sci.org/intro/article_detail/cicp/7190.html KW - AB -

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.

Francisco de la Hoz & Fernando Vadillo. (2020). A Sylvester-Based IMEX Method Via Differentiation Matrices for Solving Nonlinear Parabolic Equations. Communications in Computational Physics. 14 (4). 1001-1026. doi:10.4208/cicp.050612.180113a
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