A modified domain decomposition spectral collocation method for parabolic partial differential equations-Reference-Cited by-同舟云学术

A modified domain decomposition spectral collocation method for parabolic partial differential equations

Published:2024 Issue:3 Volume:19 Page:923-939
ISSN:1556-1801
Container-title:Networks and Heterogeneous Media
language:
Short-container-title:NHM

Author:

Luo Wei-Hua¹²,Yin Liang³,Guo Jun⁴

Affiliation:

1. School of Mathematics and Physics, Hunan University of Arts and Science, Changde, Hunan 415000, P.R. China

2. Laboratory of Numerical Simulation of Sichuan Provincial Universities, Neijiang Normal University, Neijiang, Sichuan, 641000, P.R. China

3. College of Mechanical Engineering, Hunan University of Arts and Science, Changde, Hunan, 415000, P.R. China

4. College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, Sichuan, 610225, P.R. China

Abstract

<p>In this paper, utilizing Legendre polynomials as the basis functions in both space and time, we present a modified domain decomposition spectral method for 2-dimensional parabolic partial differential equations. For solving the obtained linear/nonlinear algebraic equations, a dimension expanding preconditioner is applied employing the obtained saddle construction of the coefficient matrix. Numerical examples are given to show the performance of the presented method and the efficiency of the preconditioner.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

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