A residual method using Bézier curves for singular nonlinear equations of Lane-Emden type

ADIYAMAN M., ÖĞER V.

Kuwait Journal of Science, vol.44, no.4, pp.9-18, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 44 Issue: 4
  • Publication Date: 2017
  • Journal Name: Kuwait Journal of Science
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.9-18
  • Keywords: Bezier curves, Bernstein polynomials, continuous linear approximation, Lane-Emden equations, singular nonlinear differential equations, LEAST-SQUARES METHODS, SOLVING DIFFERENTIAL-EQUATIONS, CONTROL POINTS, 2ND KIND, APPROXIMATION, ASTROPHYSICS, ALGORITHM
  • Dokuz Eylül University Affiliated: Yes

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.