A New Sixth-Order Runge - Kutta - Nystro ̈m Method for Special Second-Order Ordinary Differential Equations
Article Sidebar
-
Initial Value Problems, ODE, One Step, Order Conditions, Runge-Kutta-Nystro ̈M Methods
Abstract
This article, an explicit Runge-Kutta-Nystr m method of sixth order for solving directly second-order ordinary differential equations, is constructed. The stability property of the new method is discussed. Numerical illustrations are presented to show the efficiency of the new method by comparing it with other existing Runge-Kutta-Nystr m and Runge-Kutta methods in the scientific literature.
Full text article
References
[1]- J. C. Butcher, Numerical Methods for Ordinary Differential Equations, John Wiley & Sons, 2nd edition, 2008.
[2]- E. Hairer, S. P. Norsett, and G. Wanner, Solving ordinary differential equations I, Non stiff problems, vol. 8, Springer, Berlin, Germany, 2nd edition, 1993.
[3]- J. D. Lambert, Numerical methods for ordinary differential systems: the initial value problem. John Wiley & Sons, New York, 1991.
[4]- Chan, R. P. and Tsai, A. Y., (2010), On explicit two-derivative Runge- Kutta methods Numerical Algorithms 53 (2): 171-194.
[5]- Anastassi, Z.A. and Kosti, A.A., (2015), A 6(4) Optimized embedded Runge-Kutta-Nystrom pair for the numerical solution of periodic problems, Journal of Computational and Applied Mathematics, 275: 311-320.
[6]- Senu, N., Runge-Kutta-Nystrom methods for solving oscillatory problems, doctoral diss, Universiti Putra Malaysia, Malaysia 2010.
[7]- Bettis, D.G., (1973), Runge-Kutta-Nystrom algorithm, Celestial Mechanics 8, 229-233.
[8]- Chang, S.H, Gnepp, P.C., (1984), A direct method for the numerical solution of y"=(x, y), Calcolo21, 369-377.
[9]- Mohamed, T. S., Senu, N., Ibrahim, Z.B., and Nik Long, N.M.A., (2018). Efficient two-derivative Runge-Kutta-Nystrom methods for solving general second-order ordinary differential equations. Discrete Dynamics in Nature and Society, Hindawi, Article ID 2393015, 10 pages.
[10]- Mohamed, T. S., Fawzi,F., R. A. Habbireeh (2021). A Third Order Trigonometrically Fitted Modified Runge-Kutta Method for the Numerical Solution of Periodic IVPs, Journal of Science, Misurata University, 335-362.
Authors
Copyright (c) 2021 Journal of Pure & Applied Sciences
This work is licensed under a Creative Commons Attribution 4.0 International License.
In a brief statement, the rights relate to the publication and distribution of research published in the journal of the University of Sebha where authors who have published their articles in the journal of the university of Sebha should how they can use or distribute their articles. They reserve all their rights to the published works, such as (but not limited to) the following rights:
- Copyright and other property rights related to the article, such as patent rights.
- Research published in the journal of the University of Sebha and used in its future works, including lectures and books, the right to reproduce articles for their own purposes, and the right to self-archive their articles.
- The right to enter a separate article, or for a non-exclusive distribution of their article with an acknowledgment of its initial publication in the journal of Sebha University.
Privacy Statement The names and e-mail addresses entered on the Sabha University Journal site will be used for the aforementioned purposes only and for which they were used.