Hybrid Taylor-Lucas collocation method for numerical solution of high-order pantograph type delay differential equations with variables delays

Bayku N., Sezer M.

Applied Mathematics and Information Sciences, vol.11, no.6, pp.1795-1801, 2017 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 6
  • Publication Date: 2017
  • Doi Number: 10.18576/amis/110627
  • Journal Name: Applied Mathematics and Information Sciences
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1795-1801
  • Keywords: Collocation method, Delay differential equation, Residual error estimation, Taylor and Lucas polynomials, Variable delays
  • Dokuz Eylül University Affiliated: Yes

Abstract

© 2017 NSP.In this study we consider a higher-order linear nonhomogenous pantograph type delay differential equation with variable coefficients and variables delays, and propose a new collocation method based on hybrid Taylor and Lucas polynomials. The presented method transforms the delay differential equation with the initial and boundary conditions to a system of linear algebraic equations with the unknown Lucas coefficients; by finding Lucas coefficients easily, Lucas polynomial solutions are obtained. Also an error estimation technique based on residual function is developed for our method and applied to exiting problems.