### Newton-Taylor polynomial solutions of systems of nonlinear differential equations with variable coefficients

Document Type : Research Paper

Author

Department of Mathematics, Faculty of science, Qom University of Technology, Qom, Iran

Abstract

The main purpose of this paper is consider Newton-Taylor polynomial solutions method in numerical solution of nonlinear system of differential equations. We apply Newton's method to linearize it. We  found Taylor polynomial solution of the linear form. Sufficient conditions for convergence of the numerical method are given and their applicability is illustrated with some examples.In numerical examples we give two benchmark sample problems and compare the proposed method by the famous Runge-Kutta fourth-order method. These sample problems practically show some advantages of the Newton-Taylor polynomial solutions method.

Keywords

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###### Volume 12, Issue 2November 2021Pages 237-248
• Receive Date: 25 July 2019
• Revise Date: 13 February 2020
• Accept Date: 20 February 2020