Improvement by projection for integro‐differential equations

Abstract

The aim of this work is to establish an improved convergence analysis via Kulkarni method to approximate the solution of an integro‐differential equation in . We prove the following convergence orders: Kulkarni order is , and Kulkarni iterated order is . The present study extends and improves earlier results in the literature. A numerical example illustrates the theoretical results and shows the effectiveness of the method.

Three methods to solve two classes of integral equations of the second kind

“…More recently, Mennouni established an improved convergence analysis via Kulkarni method (cf. [7]) to approximate the solution of integro-differential equation in L 2 ([−1, 1], C) by using the Legendre polynomials. In [8], the author introduced an efficient Galerkin method for a class of Cauchy singular integral equations of the second kind with constant coefficients in L 2 ([0, 1], C), the author used a sequence of orthogonal finite rank projections.…”