APPROXIMATE SOLUTION OF THE DUFFING EQUATION BY USING FIRST BOUBAKER POLYNOMIALS

Yüzbaşı Ş., Yıldırım G.

3 rd International Conference on Applied Engineering and Natural Sciences, Konya, Türkiye, 20 - 23 Temmuz 2022, ss.369-378

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Basıldığı Şehir: Konya
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.369-378
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In this study, the first Boubaker collocation method is performed to solve the Duffing equation. The proposed method is based on the matrix forms of the first Boubaker polynomials and their derivatives with the evenly spaced collocation points. This method reduces the Duffing equation to an algebraic matrix equation which is a set of algebraic equations with the unknown first Boubaker coefficients. Also, an error estimation method and a residual improved method are presented. In addition, the two numerical examples are given to illustrate the efficiency of the method. A comparison is made with another method in the literature. The application of the method and the graphics are obtained by using MATLAB.