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, vol.23, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 23
  • Publication Date: 2019
  • Doi Number: 10.2298/tsci181215047g
  • Journal Name: THERMAL SCIENCE
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Hermite polynomials and series, non-linear ODE, matrix and collocation method
  • Yıldız Technical University Affiliated: Yes

Abstract

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.