A Numerical Method for Solving Nonlinear Equations Arising in Astrophysics
Z. A. Zaki1, Naeem Ahmad2, Marwa I. Ghonamy3, F. A. Abd El-Salam4, A. M. Azam5
1Z. A. Zaki *, Electrical Engineering Department, College of Engineering, Jouf University, Skaka, KSA, and also Engineering Mathematics and Physics Department, Shoubra Faculty of Engineering, Benha University, Egypt.
2Naeem Ahmad, Department of Mathematics, College of Science, Jouf University, Skaka, KSA
3Marwa I. Ghonamy, Department of Mathematics, Faculty of Science, Tabuk University, Tabuk, Saudi Arabia and also Mathematics Department, Faculty of Science, Benha University, Egypt
4F. A. Abd El-Salam, Engineering Mathematics and physics Department, Shoubra Faculty of Engineering, Benha University, Egypt.
5A. M. Azam, Civil Engineering Department, College of Engineering, Jouf University, KSA, and also Public Works Engineering Department, Mansoura University, Egypt.
Manuscript received on November 15, 2019. | Revised Manuscript received on November 23, 2019. | Manuscript published on November 30, 2019. | PP: 1075-1078 | Volume-8 Issue-4, November 2019. | Retrieval Number: C6664098319/2019©BEIESP | DOI: 10.35940/ijrte.C6664.118419
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: In this paper, a parametric cubic spline function was used to get the solution of a non-linear problem for an isothermal gas sphere. The quasi-linearization procedure was used to reduce the given problem to a sequence of linear problems, the resulting equations are modified at the singular point and are handled by using parametric cubic spline for determining the numerical results. All computations have been carried out by the Mathematica software program package. The findings of computational outcomes on those astrophysics problems confirmed that the technique is legitimate for the solution of these kinds of equations.
Keywords: Non-linear Differential Equations, Parametric Cubic Spline, Lane–Emden Equations.
Scope of the Article: Numerical Modelling of Structures.