Chebyshev配置点法解Volterra型积分微分方程  

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

作　　者：吴华[1] 张珏[1] 

机构地区：[1]上海大学理学院,上海200444

出　　处：《上海大学学报（自然科学版）》2011年第2期182-188,共7页Journal of Shanghai University:Natural Science Edition

基　　金：国家自然科学基金资助项目(60874039)

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.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.

关 键 词：Chebyshev配置点法 积分微分方程 Lagrange基函数 Chebyshev权 

分 类 号：O175.6[理学—数学]