AN OPERATIONAL METHOD FOR SOLVING THE RICCATI DIFFERENTIAL EQUATION BY USING FERMAT POLYNOMIALS

Yüzbaşı Ş., Yıldırım G.

5. INTERNATIONAL PALANDOKEN SCIENTIFIC STUDIES CONGRESS , Erzurum, Türkiye, 18 - 19 Mart 2023, ss.825-832

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Basıldığı Şehir: Erzurum
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.825-832
  • Akdeniz Üniversitesi Adresli: Evet

Özet

A new matrix method based on the Fermat polynomials is presented for solving the Riccati differential equation in this study. Firstly, the operational matrix of the Fermat polynomials is composed and by using this, the solution of the Riccati differential equation is expressed in matrix form based on the Fermat polynomials. Secondly, by using the operational matrices of integration and product and the Tau method, the Riccati differential equation is transformed into a system of nonlinear algebraic equations. As the next step, the obtained nonlinear algebraic system is solved and so we get the approximate solution of the Riccati differential equation. The presented method is applied to an example and the results are presented in table and graphs. The results of application and graphs are obtained with the help of a code written in MATLAB.