Numerical Solution of Linear integro-ordinary Differential Equations Using Taylor Series

Abstract

Taylor series is applied to treat two types of higher order linear integro-ordinary differential equations: linear Fredholm and Volterra integro-ordinary differential. In this technique Taylor series is substituted for the unknown function after differentiating both sides of linear integro-ordinary differential equation with respect to x. The required derivatives and the involved integrals have been approximated using central differences and quadrature rules respectively. The resulting algebraic equations are solved by Gauss elimination technique. Program is written in MATLAB language and examples are presented to illustrate the results of this method.