Numerical solution of singular integro-differential equations with Cauchy kernel

Abstract

The main purpose of this article is to present an approximation method of for singular integro-differential equations with Cauchy kernel in the most general form under the mixed conditions in terms of the second kind Chebyshev polynomials. This method transforms mixed singular integro-differential equations with Cauchy kernel and the given conditions into matrix equation and using the zeroes of the second kind Chebyshev polynomials, the matrix equation turns a system of linear algebraic equation. The error analysis and convergence for the proposed method is also introduced. Finally, some numerical examples are presented. © IDOSI Publications, 2011.