A new spectral meshless radial point interpolation (SMRPI) method for the two-dimensional Fredholm integral equations on general domains with error analysis

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• 作者：Hedayat Fatahi^a ; Jafar Saberi-Nadjafi^a ; Elyas Shivanian^b ; ^{shivanian@sci.ikiu.ac.ir" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Spectral meshless radial point interpolation (SMRPI) method ; Radial basis function ; Fredholm integral equation ; General domain
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2016
• 出版时间：1 March 2016
• 年：2016
• 卷：294
• 期：Complete
• 页码：196-209
• 全文大小：1107 K

文摘

In this article, we present a numerical method to solve two-dimensional Fredholm integral equations of the second kind on general domains. The method utilizes meshless and spectral collocation techniques but it is not traditional meshless collocation method. The point interpolation method with the help of strictly positive definite radial basis functions is used to construct shape functions as a basis functions in the frame of spectral collocation methods. These basis functions (shape functions) have Kronecker delta function property. Since the proposed method is meshless, it does not need any domain element and so it is independent of the geometry of the domain. The method reduces the solution of the two-dimensional integral equation to the solution of a linear system of algebraic equations. Convergence analysis with error estimates are given with full discussion. Furthermore, some numerical examples are presented to show the validity and efficiency of SMRPI.