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

Year 2015, Volume: 15 Issue: 2, 1 - 11, 30.08.2015

Ayşe Anapalı Ayşe Anapalı Yalçın Öztürk , Mustafa Gülsu

https://doi.org/10.5578/fmbd.9211
Cited By: 2

Abstract

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.

Keywords

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

References

  • 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.

Year 2015, Volume: 15 Issue: 2, 1 - 11, 30.08.2015

Ayşe Anapalı Ayşe Anapalı Yalçın Öztürk , Mustafa Gülsu

https://doi.org/10.5578/fmbd.9211
Cited By: 2

Abstract

References

  • 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.
There are 13 citations in total.

Details

Subjects Engineering
Journal Section Articles
Authors

Ayşe Anapalı This is me

Ayşe Anapalı This is me

Yalçın Öztürk

Mustafa Gülsu This is me

Publication Date August 30, 2015
Submission Date November 14, 2014
Published in Issue Year 2015 Volume: 15 Issue: 2

Cite

APA Anapalı, A., Anapalı, A., Öztürk, Y., Gülsu, M. (2015). Lineer İntegral Terim İçeren Duffing Denkleminin Shifted Chebyshev Polinomları ile Nümerik Çözümleri. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 15(2), 1-11. https://doi.org/10.5578/fmbd.9211
AMA Anapalı A, Anapalı A, Öztürk Y, Gülsu M. Lineer İntegral Terim İçeren Duffing Denkleminin Shifted Chebyshev Polinomları ile Nümerik Çözümleri. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. August 2015;15(2):1-11. doi:10.5578/fmbd.9211
Chicago Anapalı, Ayşe, Ayşe Anapalı, Yalçın Öztürk, and Mustafa Gülsu. “Lineer İntegral Terim İçeren Duffing Denkleminin Shifted Chebyshev Polinomları Ile Nümerik Çözümleri”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 15, no. 2 (August 2015): 1-11. https://doi.org/10.5578/fmbd.9211.
EndNote Anapalı A, Anapalı A, Öztürk Y, Gülsu M (August 1, 2015) Lineer İntegral Terim İçeren Duffing Denkleminin Shifted Chebyshev Polinomları ile Nümerik Çözümleri. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 15 2 1–11.
IEEE A. Anapalı, A. Anapalı, Y. Öztürk, and M. Gülsu, “Lineer İntegral Terim İçeren Duffing Denkleminin Shifted Chebyshev Polinomları ile Nümerik Çözümleri”, Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 15, no. 2, pp. 1–11, 2015, doi: 10.5578/fmbd.9211.
ISNAD Anapalı, Ayşe et al. “Lineer İntegral Terim İçeren Duffing Denkleminin Shifted Chebyshev Polinomları Ile Nümerik Çözümleri”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 15/2 (August 2015), 1-11. https://doi.org/10.5578/fmbd.9211.
JAMA Anapalı A, Anapalı A, Öztürk Y, Gülsu M. Lineer İntegral Terim İçeren Duffing Denkleminin Shifted Chebyshev Polinomları ile Nümerik Çözümleri. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2015;15:1–11.
MLA Anapalı, Ayşe et al. “Lineer İntegral Terim İçeren Duffing Denkleminin Shifted Chebyshev Polinomları Ile Nümerik Çözümleri”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 15, no. 2, 2015, pp. 1-11, doi:10.5578/fmbd.9211.
Vancouver Anapalı A, Anapalı A, Öztürk Y, Gülsu M. Lineer İntegral Terim İçeren Duffing Denkleminin Shifted Chebyshev Polinomları ile Nümerik Çözümleri. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2015;15(2):1-11.

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Numerical solutions of Troesch and Duffing equations by Taylor wavelets
Hacettepe Journal of Mathematics and Statistics
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