Title of article :
A Third-degree B-spline Collocation Scheme for Solving a Class of the Nonlinear Lane-Emden Type Equations
Author/Authors :
Parsaeitabar, Zahra Department of Mathematics - School of Mathematical Sciences - Shahrood University of Technology , Nazemi, Alireza Department of Mathematics - School of Mathematical Sciences - Shahrood University of Technology
Abstract :
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 solve the resulting problem 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 :
Singular IVPs , Lane–Emden equation , Collocation method , B-spline
Journal title :
Astroparticle Physics