Bernstein collocation method for solving nonlinear Fredholm-Volterra integrodifferential equations in the most general form.(English)Zbl 1437.65232

Summary: A collocation method based on the Bernstein polynomials defined on the interval $$[a, b]$$ is developed for approximate solutions of the Fredholm-Volterra integrodifferential equation (FVIDE) in the most general form. This method is reduced to linear FVIDE via the collocation points and quasilinearization technique. Some numerical examples are also given to demonstrate the applicability, accuracy, and efficiency of the proposed method.

MSC:

 65R20 Numerical methods for integral equations 45B05 Fredholm integral equations 45D05 Volterra integral equations 45J05 Integro-ordinary differential equations 65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
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