Exponential convergence for numerical solution of integral equations using radial basis functions

Zakieh Avazzadeh*, Mohammad Heydari, Wen Chen, G. B. Loghmani

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

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.

Original languageEnglish
Article number710437
JournalJournal of Applied Mathematics
Volume2014
DOIs
Publication statusPublished - 9 Dec 2014
Externally publishedYes

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