A High-Order Finite Difference Method for 1D Nonhomogeneous Heat Equations

被引：7

作者：

Lin, Yuan ^{[1
]}

Gao, Xuejun ^{[2
]}

Xiao, MingQing ^{[1
]}

机构：

[1] So Illinois Univ, Dept Math, Carbondale, IL 62901 USA

[2] Guangdong Univ Technol, Fac Appl Math, Guangzhou, Guangdong, Peoples R China

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2009年 / 25卷 / 02期

关键词：

heat equations; finite difference method; Bartels-Stewart method; boundary value method; unconditional stability; DIFFUSION EQUATION; SCHEMES; ACCURACY;

D O I：

10.1002/num.20345

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article a sixth-order approximation method (in both temporal and spatial variables) for solving non-homogeneous heat equations is proposed. We first develop a sixth-order finite difference approximation scheme for a two-point boundary Value problem, and then heat equation is approximated by a system of ODEs defined on spatial grid points. The ODE system is discretized to a Sylvester matrix equation via boundary value method. The obtained algebraic system is solved by a modified Bartels-Stewart method. The proposed approach is unconditionally stable. Numerical results are provided to illustrate the accuracy and efficiency of our approximation method along with comparisons with those generated by the standard second-order Crank-Nicolson scheme as well as Sun-Zhang's recent fourth-order method. (C) 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 25: 327-346, 2009

引用

页码：327 / 346

页数：20

共 26 条

[1] A TAYLOR-SERIES APPROACH TO NUMERICAL ACCURACY AND A 3RD-ORDER SCHEME FOR STRONG CONVECTIVE FLOWS [J].