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Abstract and Applied Analysis
Volume 2014, Article ID 913691, 10 pages
http://dx.doi.org/10.1155/2014/913691
Research Article

A Jacobi-Collocation Method for Second Kind Volterra Integral Equations with a Smooth Kernel

School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan, Shandong 250014, China

Received 28 May 2014; Revised 2 July 2014; Accepted 2 July 2014; Published 17 July 2014

Academic Editor: Juan J. Nieto

Copyright © 2014 Hongfeng Guo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The purpose of this paper is to provide a Jacobi-collocation method for solving second kind Volterra integral equations with a smooth kernel. This method leads to a fully discrete integral operator. First, it is shown that the fully discrete integral operator is stable in both and weighted norms. Then, the proposed approach is proved to arrive at an optimal (the most possible) convergent order in both norms. One numerical example demonstrates the efficiency and accuracy of the proposed method.