Chebyshev polynomial solutions of certain second order non-linear differential equations

KEŞAN C.

Gazi University Journal of Science, cilt.24, sa.4, ss.739-745, 2011 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 24 Sayı: 4
  • Basım Tarihi: 2011
  • Dergi Adı: Gazi University Journal of Science
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.739-745
  • Anahtar Kelimeler: Approximate solution of non-linear ordinary differential equations, Chebyshev-matrix method, Non-linear differential equations
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

The purpose of this study is to give a Chebyshev polynomial approximation for the solution of second-order non-linear differential equations with variable coefficients. For this purpose, Chebyshev matrix method is introduced. This method is based on taking the truncated Chebyshev expansions of the functions in the nonlinear differential equations. Hence, the result matrix equation can be solved and the unknown Chebyshev coefficients can be found approximately. Additionally, the mentioned method is illustrated by two examples.