NUMERICAL SOLUTIONS OF A CLASS OF NON-LINEAR ORDINARY DIFFERENTIAL EQUATIONS IN HERMITE SERIES

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Güler C., Kaya S. O., Sezer M.

THERMAL SCIENCE, cilt.23, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 23
  • Basım Tarihi: 2019
  • Doi Numarası: 10.2298/tsci181215047g
  • Dergi Adı: THERMAL SCIENCE
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Hermite polynomials and series, non-linear ODE, matrix and collocation method
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

The purpose of this paper is to present a Hermite polynomial approach for solving a high-order ODE with non-linear terms under mixed conditions. The method we used is a matrix method based on collocation points together with truncated Hermite series and reduces the solution of equation to solution of a matrix equation which corresponds to a system of non-linear algebraic equations with unknown Hermite coefficients. In addition, to illustrate the validity and applicability of the method, some numerical examples together with residual error analysis are performed and the obtained results are compared with the existing result in literature.