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Zbl 1243.65154
Dehghan, Mehdi; Salehi, Rezvan
The numerical solution of the non-linear integro-differential equations based on the meshless method. (English)
[J] J. Comput. Appl. Math. 236, No. 9, 2367-2377 (2012). ISSN 0377-0427

The paper is concerned with numerical solution of nonlinear integro-differential equations based on a moving least squares method. The material is presented as follows: the authors introduce the moving least squares method and then show how it can be applied to problems of Fredholm type. They provide a detailed error analysis. This is repeated for the Volterra-type problem. The paper concludes with some numerical examples that demonstrate the efficacy of the approach.
[Neville Ford (Chester)]

MSC 2000:: *65R20 Integral equations (numerical methods)
45D05 Volterra integral equations
45G10 Nonsingular nonlinear integral equations
47G20 Integro-differential operators
45B05 Fredholm integral equations
45J05 Integro-ordinary differential equations

Keywords: meshless method; error analysis; nonlinear integro-differential equations; moving least squares method; problems of Fredholm type; Volterra-type problem; numerical examples

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Zentralblatt MATH Berlin [Germany]