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

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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Main Authors: Hongfeng Guo, Haotao Cai, Xin Zhang
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/913691
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spelling doaj-a58f506396f84007b3f07c418b30851d2020-11-24T23:47:35ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/913691913691A Jacobi-Collocation Method for Second Kind Volterra Integral Equations with a Smooth KernelHongfeng Guo0Haotao Cai1Xin Zhang2School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan, Shandong 250014, ChinaSchool of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan, Shandong 250014, ChinaSchool of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan, Shandong 250014, ChinaThe 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.http://dx.doi.org/10.1155/2014/913691
collection DOAJ
language English
format Article
sources DOAJ
author Hongfeng Guo
Haotao Cai
Xin Zhang
spellingShingle Hongfeng Guo
Haotao Cai
Xin Zhang
A Jacobi-Collocation Method for Second Kind Volterra Integral Equations with a Smooth Kernel
Abstract and Applied Analysis
author_facet Hongfeng Guo
Haotao Cai
Xin Zhang
author_sort Hongfeng Guo
title A Jacobi-Collocation Method for Second Kind Volterra Integral Equations with a Smooth Kernel
title_short A Jacobi-Collocation Method for Second Kind Volterra Integral Equations with a Smooth Kernel
title_full A Jacobi-Collocation Method for Second Kind Volterra Integral Equations with a Smooth Kernel
title_fullStr A Jacobi-Collocation Method for Second Kind Volterra Integral Equations with a Smooth Kernel
title_full_unstemmed A Jacobi-Collocation Method for Second Kind Volterra Integral Equations with a Smooth Kernel
title_sort jacobi-collocation method for second kind volterra integral equations with a smooth kernel
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2014-01-01
description 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.
url http://dx.doi.org/10.1155/2014/913691
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AT haotaocai ajacobicollocationmethodforsecondkindvolterraintegralequationswithasmoothkernel
AT xinzhang ajacobicollocationmethodforsecondkindvolterraintegralequationswithasmoothkernel
AT hongfengguo jacobicollocationmethodforsecondkindvolterraintegralequationswithasmoothkernel
AT haotaocai jacobicollocationmethodforsecondkindvolterraintegralequationswithasmoothkernel
AT xinzhang jacobicollocationmethodforsecondkindvolterraintegralequationswithasmoothkernel
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