A Mechanical Quadrature Method for Solving Delay Volterra Integral Equation with Weakly Singular Kernels

A Mechanical Quadrature Method for Solving Delay Volterra Integral Equation with Weakly Singular Kernels

In this work, a mechanical quadrature method based on modified trapezoid formula is used for solving weakly singular Volterra integral equation with proportional delays. An improved Gronwall inequality is testified and adopted to prove the existence and uniqueness of the solution of the original equ...

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Main Authors: Li Zhang, Jin Huang, Yubin Pan, Xiaoxia Wen
Format: Article
Language:English
Published: Hindawi-Wiley 2019-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2019/4813802
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spelling doaj-5e5f315c074b49b4a182632fee3862b22020-11-24T21:47:22ZengHindawi-WileyComplexity1076-27871099-05262019-01-01201910.1155/2019/48138024813802A Mechanical Quadrature Method for Solving Delay Volterra Integral Equation with Weakly Singular KernelsLi Zhang0Jin Huang1Yubin Pan2Xiaoxia Wen3School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, ChinaSchool of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, ChinaSchool of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, ChinaSchool of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, ChinaIn this work, a mechanical quadrature method based on modified trapezoid formula is used for solving weakly singular Volterra integral equation with proportional delays. An improved Gronwall inequality is testified and adopted to prove the existence and uniqueness of the solution of the original equation. Then, we study the convergence and the error estimation of the mechanical quadrature method. Moreover, Richardson extrapolation based on the asymptotic expansion of error not only possesses a high accuracy but also has the posterior error estimate which can be used to design self-adaptive algorithm. Numerical experiments demonstrate the efficiency and applicability of the proposed method.http://dx.doi.org/10.1155/2019/4813802
collection DOAJ
language English
format Article
sources DOAJ
author Li Zhang
Jin Huang
Yubin Pan
Xiaoxia Wen
spellingShingle Li Zhang
Jin Huang
Yubin Pan
Xiaoxia Wen
A Mechanical Quadrature Method for Solving Delay Volterra Integral Equation with Weakly Singular Kernels
Complexity
author_facet Li Zhang
Jin Huang
Yubin Pan
Xiaoxia Wen
author_sort Li Zhang
title A Mechanical Quadrature Method for Solving Delay Volterra Integral Equation with Weakly Singular Kernels
title_short A Mechanical Quadrature Method for Solving Delay Volterra Integral Equation with Weakly Singular Kernels
title_full A Mechanical Quadrature Method for Solving Delay Volterra Integral Equation with Weakly Singular Kernels
title_fullStr A Mechanical Quadrature Method for Solving Delay Volterra Integral Equation with Weakly Singular Kernels
title_full_unstemmed A Mechanical Quadrature Method for Solving Delay Volterra Integral Equation with Weakly Singular Kernels
title_sort mechanical quadrature method for solving delay volterra integral equation with weakly singular kernels
publisher Hindawi-Wiley
series Complexity
issn 1076-2787
1099-0526
publishDate 2019-01-01
description In this work, a mechanical quadrature method based on modified trapezoid formula is used for solving weakly singular Volterra integral equation with proportional delays. An improved Gronwall inequality is testified and adopted to prove the existence and uniqueness of the solution of the original equation. Then, we study the convergence and the error estimation of the mechanical quadrature method. Moreover, Richardson extrapolation based on the asymptotic expansion of error not only possesses a high accuracy but also has the posterior error estimate which can be used to design self-adaptive algorithm. Numerical experiments demonstrate the efficiency and applicability of the proposed method.
url http://dx.doi.org/10.1155/2019/4813802
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AT yubinpan amechanicalquadraturemethodforsolvingdelayvolterraintegralequationwithweaklysingularkernels
AT xiaoxiawen amechanicalquadraturemethodforsolvingdelayvolterraintegralequationwithweaklysingularkernels
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AT jinhuang mechanicalquadraturemethodforsolvingdelayvolterraintegralequationwithweaklysingularkernels
AT yubinpan mechanicalquadraturemethodforsolvingdelayvolterraintegralequationwithweaklysingularkernels
AT xiaoxiawen mechanicalquadraturemethodforsolvingdelayvolterraintegralequationwithweaklysingularkernels
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