TY  - JOUR
T1  - Chebyshev Polynomial Solutions of Certain Second Order Non-Linear Differential Equations
AU  - Kesan, Cenk
PY  - 2011
DA  - December
JF  - Gazi University Journal of Science
PB  - Gazi University
WT  - DergiPark
SN  - 2147-1762
SP  - 739
EP  - 745
VL  - 24
IS  - 4
LA  - en
AB  - 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.  
KW  - Non-linear differential equations
KW  - Chebyshev-matrix method
KW  - Approximate solution of non-linear
CR  - Günhan, B.C., “Approximate solutions of non-linear differential and Integral equations by Chebyshev method”, Dissertation, Dokuz Eylül University, (2001).
CR  - Keşan, C., “Taylor polynomial solutions of linear differential equations”, Appl. Math. Comput., 142: 155-165(2003).
CR  - Köroğlu, H., “Chebyshev series solution of linear Fredholm integrodifferential equations”, Int. J. Math. Educ. Sci. Technol., 29 (4): 489-500(1998).
UR  - https://dergipark.org.tr/en/pub/gujs/issue//97320
L1  - https://dergipark.org.tr/en/download/article-file/83452
ER  -