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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 | ||
| تاریخ دریافت: 03 مرداد 1398، تاریخ بازنگری: 24 بهمن 1398، تاریخ پذیرش: 01 اسفند 1398 | ||
| 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 | ||
| مراجع | ||
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[1] K. Atkinson and W. Han, Theoritical Numerical Analysis, Springer, New York, 2001.[2] B. Babayar-Razlighi and B. Soltanalizadeh, Numerical solution of nonlinear singular Volterra integral system by the Newton-Product integration method, Math. Comput. Model. 58 (2013) 1696–1703. [3] B. Babayar-Razlighi, Extrapolation method for Numerical solution of a model for endemic infectious diseases, Mathematical Researches 5 (1) (2019) 29–38 (In Persian). [4] B. Babayar-Razlighi, K. Ivaz and M. R. Mokhtarzadeh, Newton-Product Integration for a Stefan Problem with Kinetics, J. Sci. I. R. of Iran 22(1) (2011) 51–61. [5] M. Berger, Nonlinearity and Functional Analysis, Academic Press, New York, 1997. [6] H. Brunner, Implicitly linear collocation methods for nonlinear Volterra equations, Appl. Numer. Math. 9 (1992)235-247. [7] R.L. Burden and J.D. Faires, Numerical Methods, 3st ed., Thomson/Brooks/Cole, 2003. [8] E.A. Coddington and N. Levinson, Theory of Ordinary Differential Equations, McGraw Hill, New York, 1955. [9] L.M. Delves and J.L. Mohamed, Computational methods for integral equations, Cambridge University Press, 1985. [10] L. Kantorovich, and G. Akilov, Nonlinearity and Functional Analysis in Normed Spaces. 2nd ed, Pergamon Press, NewYork, 1982. [11] P. Linz, Analytical and numerical methods for Volterra equations, SIAM Philadelphia, 1985. [12] P. Linz, Theoretical numerical Analysis, John Wiley and sons Inc., 1979. [13] K. Maleknejad and M. Hadizadeh, Numerical Study of nonlinear Volterra integro-differential equations by Adomian’s method, J. Sci. I.R. Iran 9 (1998) 51–58. [14] M. Sezer, A. Karamete and M. Gulsu, Taylor polynomial solutions of systems of linear differential equations with variable coefficients, Int. J. Comput. Math. 82(6) (2005) 755-764. [15] E. Zeidler, Nonlinear Functional analysis and its applications. I: Fixed point Theorems, Springer-Verlog, New York,1985. | ||
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