Numerical simulation for the initial-boundary value problem of the Klein-Gordon-Zakharov equations

Chen, Juan; Zhang, Luming

doi:10.1007/s10255-011-0066-x

Cited by 12 publications

(8 citation statements)

References 20 publications

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“…In the Ref. [16][17][18][19], the finite difference scheme is proposed for the initial-boundary problem of the Klein-Gordon-Zakharov equations.…”

Section: ( )mentioning

confidence: 99%

The Klein–Gordon–Zakharov equations with the positive fractional power terms and their exact solutions

Zhang

2016

Pramana - J Phys

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Abstract:In this paper, the famous Klein-Gordon-Zakharov equations are firstly generalized, the new special types of Klein-Gordon-Zakharov equations with the positive fractional power terms (gKGZE) are presented. In order to derive the exact solutions of new special gKGZE, the subsidiary higher order ordinary differential equations (sub-ODEs) with the positive fractional power terms are introduced, and with the aids of the Sub-ODE, the exact solutions of three special types of the gKGZE are derived, which are the bell-type solitary wave solution, the algebraic solitary wave solution, the kink-type solitary wave solution and the sinusoidal traveling wave solution, provided that the coefficients of gKGZE satisfy certain constraint conditions.

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“…In the Ref. [16][17][18][19], the finite difference scheme is proposed for the initial-boundary problem of the Klein-Gordon-Zakharov equations.…”

Section: ( )mentioning

confidence: 99%

The Klein–Gordon–Zakharov equations with the positive fractional power terms and their exact solutions

Zhang

2016

Pramana - J Phys

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“…Due to the fast decay of the solutions of KGZ at the far field [1,2,[11][12][13][14][15], from numerical aspects, we truncate the whole space problem onto a finite interval = (a, b) in 1D with zero boundary conditions, that is,…”

Section: A Numerical Schemementioning

confidence: 99%

“…The nondimensional Klein–Gordon–Zakharov (KGZ) system in d ‐dimensions (

d = 1, 2, 3

) reads as the following,

\partial_{t t} ψ (x, t) - Δ ψ (x, t) + ψ (x, t) + ψ (x, t) ϕ (x, t) + λ | ψ |^{2} ψ (x, t) = 0,

\partial_{t t} ϕ (x, t) - Δ ϕ (x, t) - Δ (| ψ (x, t) |^{2}) = 0, x \in ℝ^{d}, t > 0,

with given initial conditions

ψ (x, 0) = ψ^{(0)} (x), \partial_{t} ψ (x, 0) = ψ^{(1)} (x), ϕ (x, 0) = ϕ^{(0)} (x), \partial_{t} ϕ (x, 0) = ϕ^{(1)} (x

…”

Section: Introductionmentioning

confidence: 99%

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On error estimates of an exponential wave integrator sine pseudospectral method for theKlein–Gordon–Zakharov system

Zhao

2015

Numerical Methods Partial

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In this article, we propose an exponential wave integrator sine pseudospectral (EWI‐SP) method for solving the Klein–Gordon–Zakharov (KGZ) system. The numerical method is based on a Deuflhard‐type exponential wave integrator for temporal integrations and the sine pseudospectral method for spatial discretizations. The scheme is fully explicit, time reversible and very efficient due to the fast algorithm. Rigorous finite time error estimates are established for the EWI‐SP method in energy space with no CFL‐type conditions which show that the method has second order accuracy in time and spectral accuracy in space. Extensive numerical experiments and comparisons are done to confirm the theoretical studies. Numerical results suggest the EWI‐SP allows large time steps and mesh size in practical computing. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 266–291, 2016

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“…In [4] Guo and Yuan studied the global smooth solutions for the Cauchy problem of these equations. Furthermore, in [5,6] the authors proposed three difference schemes for the KGZ equations. It is well known that a conservative scheme performs better than a nonconservative one; for example, Zhang et al in [7] pointed out that the nonconservative schemes may easily show nonlinear blowup and Li and Vu-Quoc also said, "in some areas, the ability to preserve some invariant properties of the original differential equation is a criterion to judge the success of a numerical simulation" (see [8]).…”

Section: Introductionmentioning

confidence: 99%

Two Energy Conserving Numerical Schemes for the Klein-Gordon-Zakharov Equations

Chen

Zhang

2013

Journal of Applied Mathematics

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Two new difference schemes are proposed for an initial-boundary-value problem of the Klein-Gordon-Zakharov (KGZ) equations. They have the advantage that there is a discrete energy which is conserved. Their stability and convergence of difference solutions are proved in order O(ℎ 2 + 2 ) on the basis of the prior estimates. Results of numerical experiments demonstrate the efficiency of the new schemes.

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Numerical simulation for the initial-boundary value problem of the Klein-Gordon-Zakharov equations

Cited by 12 publications

References 20 publications

The Klein–Gordon–Zakharov equations with the positive fractional power terms and their exact solutions

The Klein–Gordon–Zakharov equations with the positive fractional power terms and their exact solutions

On error estimates of an exponential wave integrator sine pseudospectral method for theKlein–Gordon–Zakharov system

Two Energy Conserving Numerical Schemes for the Klein-Gordon-Zakharov Equations

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