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On numerical solutions of periodically perturbed conservative systems

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Abstract

A nonlinear perturbed conservative system is discussed. By means of Hadamard's theorem, the existence and uniqueness of the solution of the continuous problem are proved. When the equation is discreted on the uniform meshes, it is proved that the corresponding discrete problem has a unique solution. Finally, the accuracy of the numerical solution is considered and a simple algorithm is provided for solving the nonlinear difference equation.

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References

  1. Lazer A C, Sanches D A. On periodically perturbed conservative systems[J].Michigan Math J, 1969,16, (2): 193–200.

    MathSciNet  MATH  Google Scholar 

  2. Amaral L, Pera M P. On periodic solutions, of nonconservative systems[J].Nonlinear Analysis, 1982,6 (7): 733–743.

    Article  MathSciNet  MATH  Google Scholar 

  3. Brown K J, Lin S S. Periodically perturbed conservative systems and a global inverse function theorem[J].Nonlinear Analysis, 1980,4, (1): 193–201.

    Article  MathSciNet  MATH  Google Scholar 

  4. Meyer G H. On solving nonlinear equations with a one-parameter operator imbedding[J].SIAM J Numer Anal, 1968,5 (4): 739–752.

    Article  MathSciNet  MATH  Google Scholar 

  5. Lazer A C. Application of lemma on bilinear forms to a problem in nonlinear Oscillations[J].Proc Amer Math Soc, 1972,33, (1): 89–94.

    Article  MathSciNet  MATH  Google Scholar 

  6. Dunford V, Schwartz J T.Linear Operator[M] Vol. II, New York: Interscience, 1963, 1289.

    Google Scholar 

  7. Hadamard J. Sur les transformation ponctuelles[J].Bull Cos Math Fr, 1906,34, (1): 71–84.

    MathSciNet  MATH  Google Scholar 

  8. Li W Shen Z. A construction proof of the periodic solution of Duffing equation[J].Chinese Science Bulletin, 1997,22 (42): 1591–1594.

    Google Scholar 

  9. Plastick R. Homeomorphism between Banach space[J].Trans Amer Math Soc, 1974,200 (1): 169–183.

    Article  MathSciNet  Google Scholar 

  10. Raduiescu M, Raduiescu S. Global inversion theorems and applications to differential equations [J].Nonlinear Analysis, 1980,4 (4): 951–965.

    Article  MathSciNet  Google Scholar 

  11. Shen Z. On the periodic solution to the Newtonian equation of motion[J].Nonlinear Analysis, 1989,13 (2): 145–149.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Basic Science, Nanjing University of Chemical Technology, 210009, Nanjing, P R China

    Liu Guo-qing Professor, Doctor

  2. Department of Mathematics, Nanjing University, 210093, Nanjing, P R China

    Fu Dong-sheng & Shen Zu-he

Authors
  1. Liu Guo-qing Professor, Doctor
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  2. Fu Dong-sheng
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  3. Shen Zu-he
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Additional information

Communicated by SU Yu-cheng

Biography: LIU Guo-qing (1966-)

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Guo-qing, L., Dong-sheng, F. & Zu-he, S. On numerical solutions of periodically perturbed conservative systems. Appl Math Mech 23, 226–235 (2002). https://doi.org/10.1007/BF02436565

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  • DOI: https://doi.org/10.1007/BF02436565

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