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

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 L∞ and weighted L2 nor...

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Bibliographic Details
Published inAbstract and Applied Analysis Vol. 2014; no. 2014; pp. 525 - 534-1555
Main Authors Guo, Hongfeng, Zhang, Xin, Cai, Haotao
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Limiteds 01.01.2014
Hindawi Publishing Corporation
John Wiley & Sons, Inc
Hindawi Limited
Subjects
Algorithms
Integral equations
Mathematical functions
Mathematical research
Science
Smoothing (Statistics)
Studies
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Summary: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 L∞ and weighted L2 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.
ISSN:1085-3375
1687-0409
DOI:10.1155/2014/913691