Expansion approach for solving nonlinear volterra integro-differential equationsJ. Rashidinia, A. Tahmasebi (pp. 14-27)
Abstract.In this paper, we develop and modify Taylor-series expansion method to approxi- mate a solution of nonlinear Volterra integro-differential equations (IDEs) as well as a solution of a system of nonlinear Volterra equations. By means of the nth-order Taylor-series expansion of an unknown function at an arbitrary point, a nonlinear Volterra equations can be converted approximately to a system of nonlinear equations for the unknown function itself and first n derivatives. Proposed method enables us to control truncation error by adjusting the step size used in the numerical scheme. The nth-order approximate solution is exact for a polynomial solution of degree equal to or less than n. Finally, error estimation of the proposed method is presented. Some numerical examples are provided to illustrate the accuracy of the method.
Keywords:integro-differential equations, approximate solution, nonlinear Volterra equations, error estimation, Taylor-series expansion method.