APPROXIMATE SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS USING CHEBYSHEV SERIES

被引：0

作者：

Arushanyan, O. B. ^{[1
]}

Volchenskova, N., I ^{[1
]}

Zaletkin, S. F. ^{[1
]}

机构：

[1] Moscow MV Lomonosov State Univ, Res Comp Ctr, Moscow 119991, Russia

来源：

SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA | 2010年 / 7卷

关键词：

ordinary differential equations; numerical methods;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

An approximate method to solve the Cauchy problem for normal and canonical systems of second-order ordinary differential equations is proposed. The method is based on orthogonal expansions of the solution and its derivative in shifted series of Chebyshev polynomials of the first kind at the integration step. The corresponding equations are constructed for the approximate values of Chebyshev coefficients in the right-hand side of the system under study. An iterative process for solving these equations is described and some sufficient conditions of its convergence are considered. Several error estimates for the Chebyshev coefficients and for the solution are given with respect to the size of the integration step.

引用

页码：122 / 131

页数：10