Klein-Gordon-Zakharov 方程的一类初边值问题的数值解

Abstract

Abstract:

In this work, a conservative difference scheme with a parameter $\theta$ is presented for the initial-boundary value problem of the Klein-Gordon-Zakharov equations. On the basis of a priori estimates, convergence of the difference solutions is proved with order O(h²+τ²) in the energy norm. Numerical experiments emonstrate the accuracy and effectiveness of the proposed scheme.

Key words: KGZ equations, Conservative difference scheme, Priori estimates, Convergence

CLC Number:

65M06

Chen Juan; Zhang Luming. Numerical Approximation of Solution for the Initial-boundary Value Problem of the Klein-Gordon-Zakharov Equations[J].Acta mathematica scientia,Series A, 2009, 29(2): 494-504.

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References

[1] Dendy R O. Plama Dynamics. Oxford: Oxford University Press, 1990

[2] Ozawa T, Tsutaya K, Tsutsumi Y. Well-posedness in energy space for the Cauchy problem of the Klein-Gordon-Zakharov equations with different propagation speeds in three space dimensions. Math Ann, 1999, 313: 127--140

[3] Guo Boling, Yuan Guangwei. Global smooth solution for the Klein-Gordon-Zakharov equations. J Math Phys, 1995, 36: 4119--4124

[4] Kimitoshi Tsutaya. Global exisitence of small amplitude solutions for the Klein-Gordon-Zakharov equations.
Non Anal, 1996, 27: 1373--1380

[5] Adomian G. Non-perturbative solution of the Klein-Gordon-Zakharov equations. Appl Math Comput, 1997, 81: 89--92

[6] Payne G L, Nicholson D R, Downie R M. Numerical solution of the Zakharov equations. J Comput Phys, 1983, 50: 482--498

[7] Glassey R T. Convergence of an energy-preserving scheme for the Zakharov equations in one space dimension. Math Comput, 1992, 58: 83--102

[8] Glassey R T. Approximate solutions to the Zakharov equations via finite differences. J Comput Phys, 1992, 100: 377--383

[9] Chang Qianshun, Jiang Hong. A conservative difference scheme for the Zakharov equations. J Comput Phys, 1994, 113: 309--319

[10] Chang Qianshun, Guo Boling, Jiang Hong. Finite difference method for the generalized Zakharov equations. Math Comput, 1995, 64: 537--553

[11] Zhang Luming. Convergence of a conservative difference scheme for a class of Klein-Gordon-Schrödinger
equations in one space dimension. Appl Math Comput, 2005, 163: 343--355

[12] Zhang L, Chang Q. Convergence and stability of a conservative finite difference scheme for a class of equation system in interaction of complex Schr\"{o}dinger field and real Klein-Gordon field. Num Math J Chinese Univ, 2000, 22(3): 362--370

[13] Zhang Luming, Chang Qenshun. A conservative nine points finite difference scheme for the Sine-Gordon equation. Math Appl, 1999, 12(3): 30--35

[14] Zhang Fei, Luis Vazquez. Two energy conserving numerical schemes for the Sine-Gordon equation. Appl Math Comput, 1991, 45: 17--30

[15] Guo Ben Yu, Pascual P J, Rodriguez M J, Luis Vazquez. Numerical solution of the Sine-Gordon equation. Appl Math Comput, 1986, 18: 1--14

[16] Zhou Y L. Application of Discrete Functional Analysis to the Finite Difference Method. Beijing: International Academic Publishers, 1990

[17] Liu Shikuo, Fu Zuntao, Liu Shida, Wang Zhanggui. The periodic solutions for a class of coupled nonlinear Klein-Gordon equations. Phys Lett A, 2004, 323: 415--420

[18] Liu Shikuo, Fu Zuntao, Liu Shida, Zhao Qiang. Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations. Phys Lett A, 2001, 289: 69--74

Numerical Approximation of Solution for the Initial-boundary Value Problem of the Klein-Gordon-Zakharov Equations

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