Lineer İntegral Terim İçeren Duffing Denkleminin Shifted Chebyshev Polinomları ile Nümerik Çözümleri

Yıl 2015, Cilt: 15 Sayı: 2, 1 - 11, 30.08.2015

Ayşe Anapalı Ayşe Anapalı Yalçın Öztürk , Mustafa Gülsu

https://doi.org/10.5578/fmbd.9211

Cited By: 2

Öz

Bu çalışmanın amacı linear terim içeren Duffing-van der Pol denkleminin shifted Chebyshev
polinomları yardımı ile yaklaşık çözümlerini sunmaktır. Bu amaçla Chebyshev sıralama
metodu verilmiştir. Metodun ana karekteristiği verilen denklemi kesilmiş Chebyshev
serisinin katasyılarının içeren bir denklem sistemine indirgemesidir. Bu sistem çözülerek
kesilmiş Chebyshev serisinin katsayıları bulunur. Dolayısıyla yaklaşık çözüm elde edilir.
Ayrıca, metodun uygulanabilirlini göstermek için örnekler sunulmuştur.

Anahtar Kelimeler

Duffing-Van der Pol denklemi, Duffing denklemi, Shifted Chebyshev Polinomları, Chebyshev serisi, Shifted Chebyshev polinom çözümleri, Yaklaşım metodu

Kaynakça

• Mickens, R.E., 1981. An Introduction to Nonlinear Oscillations, Cambridge Univ. Press, New York.
• Guckenheimer, J., Holmes, P., 1983. Oscillations, Systems, and Bifurcations of Vector Fields, Springer-Verlag, New York.
• Ahmad, B., Alghamdi, B., 2007. Extended versions of quasilinearization for the forced Communications on Applied Nonlinear Analysis, 4 (14), 67–75. equation.
• Tang, C.L., 1998,Solvability of the forced Duffing equation at resonance. Journal of Applications, 219, 110–124. Analysis and
• Ahmad, B., Alghamdi, B.S., 2008. Approximation of solutions of the nonlinear Duffing equation involving both integral and non-integral forcing terms conditions. Commucations, 179, 409–416. Physiscs
• Yao, H., 2009. Solution of the Duffing equation involving both integral and non-integralforcing terms. Computer Physiscs Communications, 180, 1481- 1488.
• Geng, F., 2011. Numerical solutions of Duffing integral and non-integral forcing terms, Computer Applications, 61:1935-1938. both Mathematics and
• Geng, F., Cui, M., 2009. New method based on the HPM and RKHSM for solving forced Duffing equations with integral boundary conditions. Journal of Computational Applied Mathematics, 233, 165-172.
• Rivlin, T.J., 1969. Introduction to the Approximation of Functions, London.
• Davis, P.J., 1963. Interpolation and Approximation, New York . Publications,
• Body, J. P., 2000. Chebyshev and Fourier Spectral Michigan, New York University of
• Atkinson, K., 2009. W. Han, Theoretical Numerical Analysis, Third Edition, Springer.
• Mason, J. C., Handscomb, D. C., 2003. Chebyshev Polynomials, Chapman and Hall/CRC, New York.