On Numerical Solutios of Periodically Perturbed Conservative Systems

LIU Guo-qing; FU Dong-sheng; SHEN Zu-he

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Article Navigation > Applied Mathematics and Mechanics > 2002 > 23(2): 207-216

LIU Guo-qing, FU Dong-sheng, SHEN Zu-he. On Numerical Solutios of Periodically Perturbed Conservative Systems[J]. Applied Mathematics and Mechanics, 2002, 23(2): 207-216.

Citation:

LIU Guo-qing, FU Dong-sheng, SHEN Zu-he. On Numerical Solutios of Periodically Perturbed Conservative Systems[J]. Applied Mathematics and Mechanics, 2002, 23(2): 207-216.

Citation:

LIU Guo-qing, FU Dong-sheng, SHEN Zu-he. On Numerical Solutios of Periodically Perturbed Conservative Systems[J]. Applied Mathematics and Mechanics, 2002, 23(2): 207-216.

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On Numerical Solutios of Periodically Perturbed Conservative Systems

1.
Department of Basic Science, Nanjing University of Chemical Technology, Nanjing 210009, P R China;
2.
Department of Mathematics, Nanjing University, Nanjing 210093, P R China

Received Date: 2000-09-29
Rev Recd Date: 2001-06-26
Publish Date: 2002-02-15

Abstract

Abstract

A nonlinear perturbed conservative system is discussed. By means of Hadamard. stheorem, 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.
- nonlinear system,
- numerical solution,
- uniqueness and existence,
- algorithm

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References(11)

References

[1]	Lazer A C,Sanches D A.On periodically perturbed conservative systems[J].Mich Math Ⅰ,1969,16(2):193-200.
[2]	Amaral L,Pera M P.On periodic solutions of nonconservative systems[J].Nonlinear Analysis,1982,6(7):733-743.
[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.
[4]	Meyer G H.On solving nonlinear equations with a one-parameter operator imbedding[J].SIAM J Numer Anal,1968,5(4):739-752.
[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.
[6]	Dunford V,Schwartz J T.Linear Operator[M].Vol Ⅱ,New York:Interscience,1963,1289.
[7]	Hadamard J.Sur les transformation ponctuelles[J].Bull Cos Math Fr,1906,34(1):71-84.
[8]	Li W,Shen Z.A construction proof of the periodic solution of Duffing equation[J].Chinese Science Bulletin,1997,22(42):1591-1594.
[9]	Plastick R.Homeomorphism between Banach space[J].Trans Amer Math Soc,1974,200(1):169-183.
[10]	Raduiescu M,Raduiescu S.Global inversion theorems and applications to differential equations[J].Nonlinear Analysis,1980,4(4):951-965.
[11]	Shen Z.On the periodic solution to the Newtonian equation of motion[J].Nonlinear Analysis,1989,13(2):145-149.