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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:
65R20Integral equations (numerical methods)
45D05Volterra integral equations
45G10Nonsingular nonlinear integral equations
47G20Integro-differential operators
45B05Fredholm integral equations
45J05Integro-ordinary differential equations
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