Numerical solution of Voltra algebraic integral equations by Taylor expansion method

Abstract

Algebraic integral equations is a special category of Volterra integral equations system, that has many applications in physics and engineering. The principal aim of this paper is to serve the numerical solution of an integral algebraic equation by using the Taylor expansion method. In this method, using the Taylor expansion of the unknown function, the algebraic integral equation system becomes a linear equation system of the unknown function and its derivatives. Moreover, the convergence analysis of this method will be shown by preparing some theorems. Several examples are included to illustrate the efficiency and accuracy of the proposed technique and also the results are compared with the different methods.