Optimal error estimates of the Legendre-Petrov-Galerkin method for the Korteweg-de Vries equation
Optimal error estimates of the Legendre-Petrov-Galerkin method for the Korteweg-de Vries equation
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DOI：
10.1137/s0036142900378327
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发表时间：
2001-12-04
影响因子：
2.9
通讯作者：
Sun, WW
中科院分区：
文献类型：
--
作者：
Ma, HP;Sun, WW
本文研究了非周期边界条件下Korteweg de弗里斯方程的Legendre-Petrov-Galerkin方法。非线性项分别用勒让德谱方法和一些伪谱方法计算。对于半离散格式和全离散格式，得到了L-2模下的最优误差估计。该方法也适用于某些（2 m + 1）阶微分方程。
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.