Compact schemes for Korteweg-de Vries equation
نویسندگان
چکیده
منابع مشابه
Multisymplectic box schemes and the Korteweg–de Vries equation
We develop and compare some geometric integrators for the Korteweg-de Vries equation, especially with regard to their robustness for large steps in space and time, ∆x and ∆t, and over long times. A standard, semi-explicit, symplectic finite difference scheme is found to be fast and robust. However, in some parameter regimes such schemes are susceptible to developing small wiggles. At the same i...
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where μ, ν are positive constants. This equation, in the case μ = 0, was derived independently by Sivashinsky [1] and Kuramoto [2] with the purpose to model amplitude and phase expansion of pattern formations in different physical situations, for example, in the theory of a flame propagation in turbulent flows of gaseous combustible mixtures, see Sivashinsky [1], and in the theory of turbulence...
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In this study, the localfractional variational iterationmethod (LFVIM) and the localfractional series expansion method (LFSEM) are utilized to obtain approximate solutions for Korteweg-de Vries equation (KdVE) within local fractionalderivative operators (LFDOs). The efficiency of the considered methods is illustrated by some examples. The results reveal that the suggested algorithms are very ef...
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Abstract: This study focus on the solution of the generalized Korteweg and de Vries (KdV) by using homotopy perturbation method (HPM). The HPM has the capabilities to bereave the complicated differential equation models to number of simple iterative models once the effective initial guess satisfying the boundary conditions is made and leads to generic solutions in addition to their rapid conver...
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Standard Galerkin approximations, using smooth splines on a uniform mesh, to 1-periodic solutions of the Korteweg-de Vries equation are analyzed. Optimal rate of convergence estimates are obtained for both semidiscrete and second order in time fully discrete schemes. At each time level, the resulting system of nonlinear equations can be solved by Newton's method. It is shown that if a proper ex...
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ژورنال
عنوان ژورنال: Thermal Science
سال: 2017
ISSN: 0354-9836,2334-7163
DOI: 10.2298/tsci160612071y