Optimal error estimates of the Legendre-Petrov-Galerkin method for the Korteweg-de Vries equation

被引：91
|
作者：
Ma, HP [1 ]
Sun, WW
机构：
[1] Shanghai Univ, Dept Math, Shanghai 200436, Peoples R China
[2] City Univ Hong Kong, Dept Math, Kowloon, Hong Kong, Peoples R China
[3] City Univ Hong Kong, Ctr Math Sci, Half Year Programme Numer Anal, Kowloon, Hong Kong, Peoples R China
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 2001年 / 39卷 / 04期
关键词：
Legendre-Petrov-Galerkin; pseudospectral; Korteweg-de Vries equation;
D O I：
10.1137/S0036142900378327
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, the Legendre-Petrov-Galerkin method for the Korteweg de Vries equation with nonperiodic boundary conditions is analyzed. The nonlinear term is computed with the Legendre spectral method and some pseudospectral methods, respectively. Optimal error estimates in L-2-norm are obtained for both semidiscrete and fully discrete schemes. The method is also applicable to some (2m + 1)th-order differential equations.
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页码：1380 / 1394
页数：15
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