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
收藏
页码：1434 / 1460
页数：27
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