Modified operational matrix method for second-order nonlinear ordinary differential equations with quadratic and cubic terms

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Gürbüz B., Sezer M.

International Journal of Optimization and Control: Theories and Applications, cilt.10, sa.2, ss.218-225, 2020 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 10 Sayı: 2
  • Basım Tarihi: 2020
  • Doi Numarası: 10.11121/ijocta.01.2020.00827
  • Dergi Adı: International Journal of Optimization and Control: Theories and Applications
  • Derginin Tarandığı İndeksler: Scopus, Academic Search Premier, Communication Abstracts, zbMATH, Directory of Open Access Journals, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.218-225
  • Anahtar Kelimeler: Collocation points, Laguerre polynomials and series, Nonlinear ordinary differential equations, Residual error estimation
  • Manisa Celal Bayar Üniversitesi Adresli: Evet

Özet

In this study, by means of the matrix relations between the Laguerre polynomials, and their derivatives, a novel matrix method based on collocation points is modified and developed for solving a class of second-order nonlinear ordinary differential equations having quadratic and cubic terms, via mixed conditions. The method reduces the solution of the nonlinear equation to the solution of a matrix equation corresponding to system of nonlinear algebraic equations with the unknown Laguerre coefficients. Also, some illustrative examples along with an error analysis based on residual function are included to demonstrate the validity and applicability of the proposed method.