Approximate solution of linear differential equations

Abstract

This paper presents an efficient approach for determining the solution of linear differential equations. The linear ordinary differential equation is first converted to a Volterra integral equation. By solving the resulting Volterra equation by means of Taylor’s expansion, different approaches based on differentiation and integration methods are employed to reduce the resulting integral equation to a system of linear equations for the unknown and its derivatives. The approximate solution of the linear differential equation is thereby obtained. A test example demonstrates the effectiveness of the method and gives the efficiency and high accuracy of the proposed method.