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Several Conservative Difference Schemes For The Klein-Gordon-Zakharov Equations

Posted on:2007-12-22Degree:MasterType:Thesis
Country:ChinaCandidate:J ChenFull Text:PDF
GTID:2120360185459644Subject:Computational Mathematics
Abstract/Summary:PDF Full Text Request
In this paper, the conservative difference schemes for the coupled nonlinear Klein-Gordon-Zakharov (KGZ) equations of the initial-boundary problem in one dimension are investigated. Three implicit finite difference schemes with order O ( h~2 +τ~2) are presented, and the second and the third schemes contain parametersθ,α(θ≥0.5,0 <α< 1) respectively. It can be easily proved that the three schemes are all complying with the conservative law which the continuous equations own. On the basis of the priori estimates, convergence and stability of the numerical solutions are proved by means of discrete functional analysis. These schemes are used to compute the solutions to one model problem of KGZ system, and the numerical solution of the function U n needs to be solved with iteration method but not of the function N~n. Numerical results demonstrate that the three difference schemes are accurate and efficient, and have better precision especially with suitable parametersθ,α.
Keywords/Search Tags:Klein-Gordon-Zakharov equations, finite difference schemes, energy conservation, priori estimates, parameter, convergence, stability
PDF Full Text Request
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