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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.

MSC:
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
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