Legendre collocation method for solving nonlinear differential equations

Güner A., Yalçinbaş S.

Mathematical and Computational Applications, cilt.18, sa.3, ss.521-530, 2013 (Scopus, TRDizin) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 18 Sayı: 3
  • Basım Tarihi: 2013
  • Doi Numarası: 10.3390/mca18030521
  • Dergi Adı: Mathematical and Computational Applications
  • Derginin Tarandığı İndeksler: Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.521-530
  • Anahtar Kelimeler: Legendre collocation method, Legendre collocation points, Legendre polynomials and series, Nonlinear ordinary differential equations
  • Manisa Celal Bayar Üniversitesi Adresli: Evet

Özet

In this study, a matrix method based on Legendre collocation points on interval [-1,1] is proposed for the approximate solution of the some first order nonlinear ordinary differential equations with the mixed conditions in terms of Legendre polynomials. The method by means of Legendre collocation points, transforms the differential equation to a matrix equation which corresponds to a system of nonlinear algebraic equations with unknown Legendre coefficients. Also, the method can be used for solving Riccati equation. The numerical results show the effectuality of the method for this type of equations. Comparisons are made between the obtained solution and the exact solution.