A numerical method for solutions of Lotka-Volterra predator-prey model with time-delay

YÜZBAŞI Ş., KARAÇAYIR M.

INTERNATIONAL JOURNAL OF BIOMATHEMATICS, cilt.11, sa.2, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 11 Sayı: 2
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1142/s1793524518500286
  • Dergi Adı: INTERNATIONAL JOURNAL OF BIOMATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Continuous population models, delay differential equations, Lotka-Volterra equation, inner product, residual error correction, CONTINUOUS POPULATION-MODELS, COLLOCATION APPROACH, DECOMPOSITION METHOD, EQUATIONS, SYSTEMS, SINGLE
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In this paper, we present a numerical scheme to obtain polynomial approximations for the solutions of continuous time-delayed population models for two interacting species. The method includes taking inner product of a set of monomials with a vector obtained from the problem under consideration. Doing this, the problem is transformed to a non-linear system of algebraic equations. This system is then solved, yielding coefficients of the approximate polynomial solutions. In addition, the technique of residual correction, which aims to increase the accuracy of the approximate solution by estimating its error, is discussed in some detail. The method and the residual correction technique are illustrated with two examples.