A COLLOCATION METHOD BASED ON LERCH POLYNOMIALS TO SOLVE THE PREDATORPREY MODEL

Yüzbaşı Ş., Yıldırım G.

5. INTERNATIONAL PALANDOKEN SCIENTIFIC STUDIES CONGRESS, Erzurum, Türkiye, 18 - 19 Mart 2023, ss.814-824

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Basıldığı Şehir: Erzurum
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.814-824
  • Akdeniz Üniversitesi Adresli: Evet

Özet

The main idea of this study is to obtain the approximate solutions of the predator-prey model by using a collocation method based on the Lerch polynomials. According to method, the solutions of the predator-prey model are written in matrix forms by using the Lerch polynomials. The derivatives of the approximate solutions, the nonlinear term and the conditions in the predator-prey model are also expressed in matrix forms. Thus, the predator-prey model converts to a system of algebraic matrix equation. The obtained system is solved via MATLAB and so the unknown Lerch coefficient matrix is calculated. Morever, by giving the error estimation method, the accuracy of the approximate solution is checked. Consequently, by making an application of the method, the efficiency of the method is observed. The results of application are given in the table and graphs.