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

ADIYAMAN M., ÖĞER V.

Kuwait Journal of Science, cilt.44, sa.4, ss.9-18, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 44 Sayı: 4
  • Basım Tarihi: 2017
  • Dergi Adı: Kuwait Journal of Science
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.9-18
  • Anahtar Kelimeler: 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 Üniversitesi Adresli: Evet

Özet

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.