HERMITE POLYNOMIAL APPROACH FOR SOLVING SINGULAR PERTURBATED DELAY DIFFERENTIAL EQUATIONS


YÜZBAŞI Ş., BAYKUŞ SAVAŞANERİL N.

JOURNAL OF SCIENCE AND ARTS, no.4, pp.845-854, 2020 (ESCI) identifier

  • Publication Type: Article / Article
  • Publication Date: 2020
  • Doi Number: 10.46939/j.sci.arts-20.4-a06
  • Journal Name: JOURNAL OF SCIENCE AND ARTS
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.845-854
  • Keywords: Boundary value problems, Singular perturbated delay differential equations, Hermite polynomials, collocation sechme, collocation points, SPLINE COLLOCATION METHOD, NUMERICAL-SIMULATION, SCHEME, ALGORITHM
  • Dokuz Eylül University Affiliated: Yes

Abstract

In this study, a collocation approach based on the Hermite polyomials is applied to solve the singularly perturbated delay differential eqautions by boundary conditions. By means of the matix relations of the Hermite polynomials and the derivatives of them, main problem is reduced to a matrix equation. And then, collocation points are placed in equation of the matrix. Hence, the singular perturbed problem is transformed into an algebraic system of linear equations. This system is solved and thus the coefficients of the assumed approximate solution are determined. Numerical applications are made for various values of N.