In this work, we seek the approximate solution of integral equations by truncation Legendre series approximation using a variational form for the equation. this one is reduced to a linear system where the solution of this latter gives the Legendre coefficients and thereafter the solution of the equation.The convergence and the error analysis of this method are discussed. Finally, we compare our numerical results by others.

No abstract

The aim of this work is to solve singular integral equations (S.I.E), of Cauchy type on a closed smooth curve. This method presented by the author is based on the adapted linear approximation of the singular integral of the dominant part, where we reduce a (S.I.E) to an algebraic linear system and we realize numerically this approach by examples.

No abstract