Taylor matrix method for solving linear two-dimensional Fredholm integral equations with Piecewise Intervals

Abstract

This paper contributes an efficient numerical approach, which produces an approximate polynomial solution, for solving linear two-dimensional Fredholm integral equations with piecewise intervals. The main technique is based upon approximating the unknown function (i.e., expected solution) and known functions (including four variable kernel functions and two variable source functions) in terms of their Taylor expansions in a new matrix form. With the aid of these approximations, we convert the main problems into their associated matrix equations. The matrix equations correspond to systems of linear equations with the unknown Taylor coefficients. Moreover, under several mild conditions, error analysis of the proposed method is provided. Numerical examples are included to demonstrate the validity and applicability of the method and the comparisons are made with the existing results.