A numerical method for solving systems of higher order linear functional differential equations

YÜZBAŞI Ş., Gok E., SEZER M.

OPEN PHYSICS, cilt.14, sa.1, ss.15-25, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 14 Sayı: 1
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1515/phys-2015-0052
  • Dergi Adı: OPEN PHYSICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.15-25
  • Anahtar Kelimeler: systems of functional differential equations, matrix-collocation method, Muntz-Legendre polynomials, approximate solutions, EFFICIENT ALGORITHM, COLLOCATION METHOD
  • Akdeniz Üniversitesi Adresli: Evet

Özet

Functional differential equations have importance in many areas of science such as mathematical physics. These systems are difficult to solve analytically. In this paper we consider the systems of linear functional differential equations [1-9] including the term y(alpha x + beta) and advance-delay in derivatives of y. To obtain the approximate solutions of those systems, we present a matrix-collocation method by using Muntz-Legendre polynomials and the collocation points. For this purpose, to obtain the approximate solutions of those systems, we present a matrix-collocation method by using Muntz-Legendre polynomials and the collocation points. This method transform the problem into a system of linear algebraic equations. The solutions of last system determine unknown co-efficients of original problem. Also, an error estimation technique is presented and the approximate solutions are improved by using it. The program of method is written in Matlab and the approximate solutions can be obtained easily. Also some examples are given to illustrate the validity of the method.