Laguerre Matrix-Collocation Method to Solve Systems of Pantograph Type Delay Differential Equations

Gürbüz B., Sezer M.

4th International Conference on Computational Mathematics and Engineering Sciences, CMES 2019, Antalya, Turkey, 20 - 22 April 2019, vol.1111 AISC, pp.121-132, (Full Text) identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 1111 AISC
  • Doi Number: 10.1007/978-3-030-39112-6_8
  • City: Antalya
  • Country: Turkey
  • Page Numbers: pp.121-132
  • Keywords: Collocation method, Laguerre polynomials and series, Matrix method, Pantograph equations, System of delay differential equations
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

In this study, an improved matrix method based on collocation points is developed to obtain the approximate solutions of systems of high-order pantograph type delay differential equations with variable coefficients. These kinds of systems described by the existence of linear functional argument play a critical role in defining many different phenomena and particularly, arise in industrial applications and in studies based on biology, economy, electrodynamics, physics and chemistry. The technique we have used reduces the mentioned delay system solution with the initial conditions to the solution of a matrix equation with the unknown Laguerre coefficients. Thereby, the approximate solution is obtained in terms of Laguerre polynomials. In addition, several examples along with error analysis are given to illustrate the efficiency of the method; the obtained results are scrutinized and interpreted.