Exponential Convergence for Numerical Solution of Integral Equations Using Radial Basis Functions

Exponential Convergence for Numerical Solution of Integral Equations Using Radial Basis Functions

We solve some different type of Urysohn integral equations by using the radial basis functions. These types include the linear and nonlinear Fredholm, Volterra, and mixed Volterra-Fredholm integral equations. Our main aim is to investigate the rate of convergence to solve these equations using the r...

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Main Authors: Zakieh Avazzadeh, Mohammad Heydari, Wen Chen, G. B. Loghmani
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2014/710437
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spelling doaj-99a41bee6fdc431f9841f1de204bd5b02020-11-24T23:08:41ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/710437710437Exponential Convergence for Numerical Solution of Integral Equations Using Radial Basis FunctionsZakieh Avazzadeh0Mohammad Heydari1Wen Chen2G. B. Loghmani3State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, College of Mechanics and Materials, Hohai University, Nanjing 210098, ChinaYoung Researchers and Elite Club, Islamic Azad University, Ashkezar Branch, Ashkezar 8941613695, IranState Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, College of Mechanics and Materials, Hohai University, Nanjing 210098, ChinaDepartment of Mathematics, Yazd University, P.O. Box 89195-741, Yazd, IranWe solve some different type of Urysohn integral equations by using the radial basis functions. These types include the linear and nonlinear Fredholm, Volterra, and mixed Volterra-Fredholm integral equations. Our main aim is to investigate the rate of convergence to solve these equations using the radial basis functions which have normic structure that utilize approximation in higher dimensions. Of course, the use of this method often leads to ill-posed systems. Thus we propose an algorithm to improve the results. Numerical results show that this method leads to the exponential convergence for solving integral equations as it was already confirmed for partial and ordinary differential equations.http://dx.doi.org/10.1155/2014/710437
collection DOAJ
language English
format Article
sources DOAJ
author Zakieh Avazzadeh
Mohammad Heydari
Wen Chen
G. B. Loghmani
spellingShingle Zakieh Avazzadeh
Mohammad Heydari
Wen Chen
G. B. Loghmani
Exponential Convergence for Numerical Solution of Integral Equations Using Radial Basis Functions
Journal of Applied Mathematics
author_facet Zakieh Avazzadeh
Mohammad Heydari
Wen Chen
G. B. Loghmani
author_sort Zakieh Avazzadeh
title Exponential Convergence for Numerical Solution of Integral Equations Using Radial Basis Functions
title_short Exponential Convergence for Numerical Solution of Integral Equations Using Radial Basis Functions
title_full Exponential Convergence for Numerical Solution of Integral Equations Using Radial Basis Functions
title_fullStr Exponential Convergence for Numerical Solution of Integral Equations Using Radial Basis Functions
title_full_unstemmed Exponential Convergence for Numerical Solution of Integral Equations Using Radial Basis Functions
title_sort exponential convergence for numerical solution of integral equations using radial basis functions
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2014-01-01
description We solve some different type of Urysohn integral equations by using the radial basis functions. These types include the linear and nonlinear Fredholm, Volterra, and mixed Volterra-Fredholm integral equations. Our main aim is to investigate the rate of convergence to solve these equations using the radial basis functions which have normic structure that utilize approximation in higher dimensions. Of course, the use of this method often leads to ill-posed systems. Thus we propose an algorithm to improve the results. Numerical results show that this method leads to the exponential convergence for solving integral equations as it was already confirmed for partial and ordinary differential equations.
url http://dx.doi.org/10.1155/2014/710437
work_keys_str_mv AT zakiehavazzadeh exponentialconvergencefornumericalsolutionofintegralequationsusingradialbasisfunctions
AT mohammadheydari exponentialconvergencefornumericalsolutionofintegralequationsusingradialbasisfunctions
AT wenchen exponentialconvergencefornumericalsolutionofintegralequationsusingradialbasisfunctions
AT gbloghmani exponentialconvergencefornumericalsolutionofintegralequationsusingradialbasisfunctions
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