A Residual Method Using Bézier Curves for Singular Nonlinear Equations of Lane-Emden Type

Authors

  • Meltem Adiyaman Department of Mathematics, Faculty of Sciences, Dokuz Eylul University, Tınaztepe, Buca, 35160 Izmir, Turkey
  • Volkan Oger Department of Mathematics, Faculty of Sciences, Dokuz Eylul University, Tınaztepe, Buca, 35160 Izmir, Turkey

Keywords:

Bézier curves, Bernstein polynomials, continuous linear approximation, Lane- Emden equations, singular nonlinear differential equations.

Abstract

In this article, we introduce a new method to solve a singular non-linear equation of the Lane-Emden type by approximating the solution with Bernstein polynomials. This method is based on the minimization of a residual function using Taylor’s series expansion. We also apply this method to problems that are solved by other methods and the obtained results show that
our method is efficient, applicable and has great potential than others.

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Published

01-11-2017