Numerical solution of Volterra integro-differential equations

In this study, a numerical method for solving Volterra integro-differential equations is presented. First, we convert the Volterra integro-differential equations to power series, then we transform the power series into Pade series form, which gives an arbitrary order for solving Volterra integro-differential equations. In the sequel, an efficient error estimation of the numerical solution is introduced. Some experiments and comparing it with other methods clarify the high accuracy and efficiency of the proposed method. Applying this method of solution for nonlinear Volterra integro-differential equations and computations of the run time state the excellent advantages of the method. In addition, numerical experiments indicate that the method is convergent.