Galerkin-Chebyshev spectral method and block boundary value methods for two-dimensional semilinear parabolic equations

被引：10

作者：

Liu, Wenjie ^{[1
]}

Sun, Jiebao ^{[1
]}

Wu, Boying ^{[1
]}

机构：

[1] Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China

来源：

NUMERICAL ALGORITHMS | 2016年 / 71卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Spectral method; Block boundary value methods; Semilinear parabolic equation; Error estimate; TIME-DEPENDENT COEFFICIENT; IMPLICIT RUNGE-KUTTA; HEAT;

D O I：

10.1007/s11075-015-0002-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present a high-order accurate method for two-dimensional semilinear parabolic equations. The method is based on a Galerkin-Chebyshev spectral method for discretizing spatial derivatives and a block boundary value methods of fourth-order for temporal discretization. Our formulation has high-order accurate in both space and time. Optimal a priori error bound is derived in the weighted -norm for the semidiscrete formulation. Extensive numerical results are presented to demonstrate the convergence properties of the method.

引用

页码：437 / 455

页数：19

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