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

	Newton-Taylor polynomial solutions of systems of nonlinear differential equations with variable coefficients
International Journal of Nonlinear Analysis and Applications
مقاله 18، دوره 12، شماره 2، بهمن 2021، صفحه 237-248 اصل مقاله (413.1 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2020.18371.2007
نویسنده
Bahman Babayar-Razlighi^*
Department of Mathematics, Faculty of science, Qom University of Technology, Qom, Iran
چکیده
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.
کلیدواژه‌ها
Variable coefficients؛ Newton's method؛ Taylor polynomial solutions؛ Ordinary differential equations؛ Nonlinear systems
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