Approximate Solution Of Logistic Growth Model Via Lerch Collocation Method

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Yüzbaşı Ş., Yıldırım G.

4. INTERNATIONAL SCIENTIFIC RESEARCH AND INNOVATION CONGRESS, İstanbul, Türkiye, 11 - 12 Mart 2023, ss.224-233

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Basıldığı Şehir: İstanbul
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.224-233
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In this paper, a collocation method is presented for the logistic growth model by using the Lerch polynomials. Firstly, we start by assuming the solution of the logistic growth model in truncated series form of Lerch polynomials. By using this solution form, the derivative of the solution form, the nonlinear term in the logistic growth equation and the condition are also written in matrix forms. Our method transforms the logistic growth model to a system of algebraic matrix equations which is a set of algebraic equations with the unknown Lerch coefficients. By solving this system with the help of a code written in MATLAB, the unknown coefficient matrix is obtained. Additionally, the error estimation method is presented. Thus, the accuracy of the approximate solution is checked. Finally, an application of the method is made to show the efficiency of the method. The obtained results are shown in the table and graphs.