:: Volume 12, Number 2 (9-2017) ::
IJMSI 2017, 12(2): 15-34 Back to browse issues page
A Third-degree B-spline Collocation Scheme for Solving a Class of the Nonlinear Lane–-Emden Type Equations
Z. Parsaeitabar, A. R. Nazemi
Abstract:  

In this paper, we use a numerical method involving collocation method with third B-splines as basis functions for solving a class of singular initial value problems (IVPs) of Lane--Emden type equation. The original differential equation is modified at the point of singularity. The modified problem is then treated by using B-spline approximation. In the case of non-linear problems, we first linearize the equation using quasilinearization technique and the resulting problem is solved by a third degree B-spline function. Some numerical examples are included to demonstrate the feasibility and the efficiency of the proposed technique. The method is easy to implement and produces accurate results. The numerical results are also found to be in good agreement with the exact solutions.

Keywords: B-spline, Collocation method, Lane--Emden equation, Singular IVPs.
Full-Text [PDF 188 kb]      
Type of Study: Research | Subject: General



DOI: 10.7508/ijmsi.2017.2.002


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Volume 12, Number 2 (9-2017) Back to browse issues page