A Jacobi-Collocation Method for Second Kind Volterra Integral Equations with a Smooth Kernel. (17th July 2014)

• Record Type: Journal Article
• Authors: Guo, Hongfeng; Cai, Haotao; Zhang, Xin
• Other Names: Nieto Juan J. Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2014(2014)
• Publication Date: 2014-07-17
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2014/913691
• Languages: English
• ISSNs: 1085-3375

Abstract

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 bothL ∞ and weightedL 2 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.