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Computational method based on Bernstein operational matrices for nonlinear Volterra-Fredholm-Hammerstein integral equations. (English) Zbl 1244.65243
Summary: We present a method to solve nonlinear Volterra-Fredholm-Hammerstein integral equations in terms of Bernstein polynomials. Properties of these polynomials and of the operational matrix of integration together with the product operational matrix are first presented. These properties are then utilized to transform the integral equation to a matrix equation which corresponds to a system of nonlinear algebraic equations with unknown Bernstein coefficients. The method is computationally very simple and attractive and numerical examples illustrate the efficiency and accuracy of the method.

65R20Integral equations (numerical methods)
45B05Fredholm integral equations
45D05Volterra integral equations
45G10Nonsingular nonlinear integral equations
Full Text: DOI
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