An efficient hybrid method for solving fredholm integral equations using triangular functions

Abstract

In this paper the orthogonal triangular function (TF) based method is first applied to transform the Fredholm integral equations and Fredholm system of integral equations to a coupled system of matrix algebraic equations. The obtained system is a variant of coupled Sylvester matrix equations. A finite iterative algorithm is then applied to solve this system to obtain the coefficients used to get the form of approximate solution of the unknown functions of the integral problems. Some numerical examples are solved to illustrate the accuracy and the efficiency of the proposed hybrid method. The obtained numerical results are compared with other numerical methods and the exact solutions.

Keywords

• Fredholm integral equation,triangular functions,generalized Sylvester matrix equation,generalized iterative algorithm

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