Numerical solution of a singular integro-differential equation

摘要

This paper presents a method based on polynomial approximation using Bernstein polynomial basis to obtain approximate numerical solution of a singular integro-differential equation with Cauchy kernel. The numerical results obtained by the present method compares favorably with those obtained by various Galerkin methods earlier in the literature. Also the convergence of the method is established rigorously for the studied integro-differential equation.