ON SPECTRAL METHODS FOR VOLTERRA INTEGRAL EQUATIONS AND THE CONVERGENCE ANALYSIS  

作　　者：Tao Tang Xiang XU Jin Cheng 

机构地区：[1]Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China [2]School of Mathematics, Fudan University, Shanghai 200433, China

出　　处：《Journal of Computational Mathematics》2008年第6期825-837,共13页计算数学（英文）

基　　金：supported by CERG Grants of Hong Kong Research Grant Council;FRG grants of Hong Kong Baptist University

摘　　要：The main purpose of this work is to provide a novel numerical approach for the Volterra integral equations based on a spectral approach. A Legendre-collocation method is proposed to solve the Volterra integral equations of the second kind. We provide a rigorous error analysis for the proposed method, which indicates that the numerical errors decay exponentially provided that the kernel function and the source function are sufficiently smooth. Numerical results confirm the theoretical prediction of the exponential rate of convergence. The result in this work seems to be the first successful spectral approach （with theoretical justification） for the Volterra type equations.The main purpose of this work is to provide a novel numerical approach for the Volterra integral equations based on a spectral approach. A Legendre-collocation method is proposed to solve the Volterra integral equations of the second kind. We provide a rigorous error analysis for the proposed method, which indicates that the numerical errors decay exponentially provided that the kernel function and the source function are sufficiently smooth. Numerical results confirm the theoretical prediction of the exponential rate of convergence. The result in this work seems to be the first successful spectral approach （with theoretical justification） for the Volterra type equations.

关 键 词：Legendre-spectral method Second kind Volterra integral equations Convergence analysis. 

分 类 号：O175[理学—数学]