A MULTISTEP LEGENDRE-GAUSS SPECTRAL COLLOCATION METHOD FOR NONLINEAR VOLTERRA INTEGRAL EQUATIONS

被引：66

作者：

Sheng, Chang-Tao ^{[1
]}

Wang, Zhong-Qing ^{[1
]}

Guo, Ben-Yu ^{[1
]}

机构：

[1] Shanghai Normal Univ, E Inst Shanghai Univ, Div Computat Sci, Dept Math,Sci Comp Key Lab Shanghai Univ, Shanghai 200234, Peoples R China

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2014年 / 52卷 / 04期

关键词：

multistep Legendre-Gauss spectral collocation method; nonlinear Volterra integral equations; error analysis; INITIAL-VALUE PROBLEMS; RUNGE-KUTTA METHODS; NUMERICAL-SOLUTION; HP-VERSION; TIME; STABILITY;

D O I：

10.1137/130915200

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce a multistep Legendre-Gauss spectral collocation method for the nonlinear Volterra integral equations of the second kind. This method is easy to implement and possesses high order accuracy. In addition, it is very suitable for long time calculations. We also derive the optimal convergence of the hp-version of the multistep collocation method under the L-2-norm. Numerical experiments confirm the theoretical expectations.

引用

页码：1953 / 1980

页数：28

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