Analytical solution of systems of Volterra integro-differential equations using modified differential transform method

Abstract

In this paper, a hybrid technique based on the combining of differential transform approach, the Laplace transformation, and Pade approximant is successfully implemented for solving Volterra Integro differential (VID) equations subject to appropriate conditions. The proposed method known as modified differential transform method (MDTM) enlarges the domain of convergence with less computational time. One of the interesting features of this algorithm is the ability to produce an analytic approximate solution in convergent power series form with few numbers of computable terms. Preliminary results on some test problems show that the new algorithm is efficient and promising for Volterra integro-differential equations and can be applied as alternatives for the integral and integro-differential (IID) equation that have no analytical solution.