Chebyshev配置点法解Volterra型积分微分方程

上海大学学报(自然科学版) ›› 2011, Vol. 17 ›› Issue (2): 182-188.

Chebyshev配置点法解Volterra型积分微分方程

吴华,张珏

上海大学理学院,上海 200444

收稿日期:2009-10-19 出版日期:2011-04-30 发布日期:2011-04-30
基金资助:
国家自然科学基金资助项目(60874039)

Chebyshev-Collocation Spectral Method for Volterra Type Integro-Differential Equations

WU Hua, ZHANG Jue

College of Sciences, Shanghai University, Shanghai 200444, China

Received:2009-10-19 Online:2011-04-30 Published:2011-04-30

摘要/Abstract

摘要：

采用Chebyshev配点法求解Volterra型积分微分方程，首先将Volterra型积分微分方程重新写成一个第二类的线性积分方程组，然后将方程组中的被积函数用Lagrange基函数展开,再将Lagrange基函数用Chebyshev多项式展开，在L_∞范数下作误差分析，最后用数值算例来证明该方法的可行性.

关键词: Chebyshev配置点法;积分微分方程;Lagrange基函数;Chebyshev权

Abstract:

A Chebyshev-collocation spectral method is developed for Volterra type integro-differential equations. The Volterra type integro-differential equation as two linear integral equations of the second kind is rewrited, and the integrand with Lagrange basis functions and the Lagrange basis functions in terms of the Chebyshev polynomials are expanded. An error analysis is conducted based on the L_∞ norm. Numerical results are presented to demonstrate effectiveness of the proposed method.

Key words: Chebyshev-collocation spectral method; integro-differential equations; Lagrange basis function; Chebyshev weight

中图分类号:

O 175.6

吴华,张珏. Chebyshev配置点法解Volterra型积分微分方程[J]. 上海大学学报(自然科学版), 2011, 17(2): 182-188.

WU Hua, ZHANG Jue. Chebyshev-Collocation Spectral Method for Volterra Type Integro-Differential Equations[J]. Journal of Shanghai University（Natural Science Edition）, 2011, 17(2): 182-188.