Chebyshev Polynomial Solutions of Certain Second Order Non-Linear Differential Equations

Yıl 2011, Cilt: 24 Sayı: 4, 739 - 745, 01.02.2011

Cenk Kesan

Öz

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 non-linear 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.

 

                Key Words: Non-linear differential equations, Chebyshev-

               matrix method, Approximate solution of               non-linear  

               ordinary differential equations.

 

Anahtar Kelimeler

Non-linear differential equations, Chebyshev-matrix method, Approximate solution of non-linear

Kaynakça

• Günhan, B.C., “Approximate solutions of non-linear differential and Integral equations by Chebyshev method”, Dissertation, Dokuz Eylül University, (2001).
• Keşan, C., “Taylor polynomial solutions of linear differential equations”, Appl. Math. Comput., 142: 155-165(2003).
• Köroğlu, H., “Chebyshev series solution of linear Fredholm integrodifferential equations”, Int. J. Math. Educ. Sci. Technol., 29 (4): 489-500(1998).