The numerical solution of the non-linear integro-differential equations based on the meshless method. (English) Zbl 1243.65154

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.


65R20 Numerical methods for integral equations
45D05 Volterra integral equations
45G10 Other nonlinear integral equations
47G20 Integro-differential operators
45B05 Fredholm integral equations
45J05 Integro-ordinary differential equations
Full Text: DOI


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