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2014 Exponential Convergence for Numerical Solution of Integral Equations Using Radial Basis Functions
Zakieh Avazzadeh, Mohammad Heydari, Wen Chen, G. B. Loghmani
J. Appl. Math. 2014: 1-9 (2014). DOI: 10.1155/2014/710437

Abstract

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.

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Zakieh Avazzadeh. Mohammad Heydari. Wen Chen. G. B. Loghmani. "Exponential Convergence for Numerical Solution of Integral Equations Using Radial Basis Functions." J. Appl. Math. 2014 1 - 9, 2014. https://doi.org/10.1155/2014/710437

Information

Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07131813
MathSciNet: MR3293000
Digital Object Identifier: 10.1155/2014/710437

Rights: Copyright © 2014 Hindawi

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