Abstract
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.
Keywords
Non-linear differential equations Chebyshev-matrix method Approximate solution of non-linear
References
- 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).
Abstract
References
- 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).
Details
| Primary Language | English |
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| Journal Section | Mathematics |
| Authors | |
| Publication Date | February 1, 2011 |
| Published in Issue | Year 2011 Volume: 24 Issue: 4 |