Legendre-Gauss-type spectral collocation algorithms for nonlinear ordinary/partial differential equations

被引：11

作者：

Yi, Lijun ^{[1
,2
]}

Wang, Zhongqing ^{[1
,2
]}

机构：

[1] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

[2] Shanghai Univ E Inst, Div Computat Sci, Shanghai 200234, Peoples R China

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2014年 / 91卷 / 07期

基金：

高等学校博士学科点专项科研基金;

关键词：

spectral collocation method; time-dependent nonlinear partial differential equations; ordinary differential equations; discretization in time and space; high-order accuracy; INITIAL-VALUE PROBLEMS; PRIORI ERROR ANALYSIS; HP-VERSION; TIME; ACCURACY;

D O I：

10.1080/00207160.2013.841901

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose new Legendre-Gauss collocation algorithms for ordinary differential equations. We also design Legendre-Gauss-type collocation algorithms for time-dependent nonlinear partial differential equations. The suggested algorithms enjoy spectral accuracy in both time and space, and can be implemented in a fast and stable manner. Numerical results exhibit the effectiveness.

引用

页码：1434 / 1460

页数：27

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