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Numerical solution of some classes of integral equations using Bernstein polynomials. (English) Zbl 1122.65416

Summary: This paper is concerned with obtaining approximate numerical solutions of some classes of integral equations by using Bernstein polynomials as basis. The integral equations considered are Fredholm integral equations of second kind, a simple hypersingular integral equation and a hypersingular integral equation of second kind. The method is explained with illustrative examples. Also, the convergence of the method is established rigorously for each class of integral equations considered here.

MSC:

65R20 Numerical methods for integral equations
45B05 Fredholm integral equations
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
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