Convergence Analysis of Generalized Jacobi-Galerkin Methods for Second Kind Volterra Integral Equations with Weakly Singular Kernels

Convergence Analysis of Generalized Jacobi-Galerkin Methods for Second Kind Volterra Integral Equations with Weakly Singular Kernels

We develop a generalized Jacobi-Galerkin method for second kind Volterra integral equations with weakly singular kernels. In this method, we first introduce some known singular nonpolynomial functions in the approximation space of the conventional Jacobi-Galerkin method. Secondly, we use the Gauss-J...

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Main Author: Haotao Cai
Format: Article
Language:English
Published: Hindawi Limited 2017-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2017/4751357
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spelling doaj-c958d0b3edd844b08255e794d96975b12020-11-24T21:04:46ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882017-01-01201710.1155/2017/47513574751357Convergence Analysis of Generalized Jacobi-Galerkin Methods for Second Kind Volterra Integral Equations with Weakly Singular KernelsHaotao Cai0School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan, Shandong 250014, ChinaWe develop a generalized Jacobi-Galerkin method for second kind Volterra integral equations with weakly singular kernels. In this method, we first introduce some known singular nonpolynomial functions in the approximation space of the conventional Jacobi-Galerkin method. Secondly, we use the Gauss-Jacobi quadrature rules to approximate the integral term in the resulting equation so as to obtain high-order accuracy for the approximation. Then, we establish that the approximate equation has a unique solution and the approximate solution arrives at an optimal convergence order. One numerical example is presented to demonstrate the effectiveness of the proposed method.http://dx.doi.org/10.1155/2017/4751357
collection DOAJ
language English
format Article
sources DOAJ
author Haotao Cai
spellingShingle Haotao Cai
Convergence Analysis of Generalized Jacobi-Galerkin Methods for Second Kind Volterra Integral Equations with Weakly Singular Kernels
Journal of Function Spaces
author_facet Haotao Cai
author_sort Haotao Cai
title Convergence Analysis of Generalized Jacobi-Galerkin Methods for Second Kind Volterra Integral Equations with Weakly Singular Kernels
title_short Convergence Analysis of Generalized Jacobi-Galerkin Methods for Second Kind Volterra Integral Equations with Weakly Singular Kernels
title_full Convergence Analysis of Generalized Jacobi-Galerkin Methods for Second Kind Volterra Integral Equations with Weakly Singular Kernels
title_fullStr Convergence Analysis of Generalized Jacobi-Galerkin Methods for Second Kind Volterra Integral Equations with Weakly Singular Kernels
title_full_unstemmed Convergence Analysis of Generalized Jacobi-Galerkin Methods for Second Kind Volterra Integral Equations with Weakly Singular Kernels
title_sort convergence analysis of generalized jacobi-galerkin methods for second kind volterra integral equations with weakly singular kernels
publisher Hindawi Limited
series Journal of Function Spaces
issn 2314-8896
2314-8888
publishDate 2017-01-01
description We develop a generalized Jacobi-Galerkin method for second kind Volterra integral equations with weakly singular kernels. In this method, we first introduce some known singular nonpolynomial functions in the approximation space of the conventional Jacobi-Galerkin method. Secondly, we use the Gauss-Jacobi quadrature rules to approximate the integral term in the resulting equation so as to obtain high-order accuracy for the approximation. Then, we establish that the approximate equation has a unique solution and the approximate solution arrives at an optimal convergence order. One numerical example is presented to demonstrate the effectiveness of the proposed method.
url http://dx.doi.org/10.1155/2017/4751357
work_keys_str_mv AT haotaocai convergenceanalysisofgeneralizedjacobigalerkinmethodsforsecondkindvolterraintegralequationswithweaklysingularkernels
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