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Hybrid Legendre polynomials and block-pulse functions approach for nonlinear Volterra-Fredholm integro-differential equations. (English) Zbl 1221.65333

Summary: This paper introduces an approach for obtaining the numerical solution of the nonlinear Volterra-Fredholm integro-differential (NVFID) equations using hybrid Legendre polynomials and block-pulse functions. These hybrid functions and their operational matrices are used for representing matrix form of these equations. The main characteristic of this approach is that it reduces NVFID equations to a system of algebraic equations, which greatly simplifying the problem. Numerical examples illustrate the validity and applicability of the proposed method.

MSC:

65R20 Numerical methods for integral equations
45J05 Integro-ordinary differential equations
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