Journal ArticleDOI
Petrov-Galerkin methods for nonlinear dispersive waves
TLDR
In this article, Petrov-Galerkin methods based on piecewise linear interpolants for the Korteweg-de Vries and related equations are studied and both accuracy and stability are analyzed for the linearised case.About:
This article is published in Journal of Computational Physics.The article was published on 1981-01-01. It has received 115 citations till now. The article focuses on the topics: Discontinuous Galerkin method & Galerkin method.read more
Citations
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Journal ArticleDOI
A numerical study of compactons
M. S. Ismail,Thiab R. Taha +1 more
TL;DR: In this paper, a single compacton as well as the interaction of compactons have been studied and the numerical results have shown that these compactons exhibit true soliton behavior, and the analytical solutions and conserved quantities are used to assess the accuracy of these methods.
Journal ArticleDOI
The group finite element formulation
TL;DR: In this article, a group finite element formulation of Burgers' equations with linear rectangular elements has been proposed to reduce execution time with a small improvement in accuracy with no loss of accuracy.
Journal ArticleDOI
Solitary waves of the regularized long-wave equation
L. R. T. Gardner,G. A. Gardner +1 more
TL;DR: In this article, a finite element solution of the Regularised Long Wave Equation, based on Galerkin's method using cubic splines as element shape functions, is set up, and a linear stability analysis shows the scheme to be unconditionally stable.
Journal ArticleDOI
Approximation of the RLW equation by the least square cubic B-spline finite element method
İdris Daǧ,M. Naci Özer +1 more
TL;DR: In this article, the regularized long wave (RLW) equation is solved numerically by giving a new algorithm based on a kind of space-time least square finite element method, in which a combination of cubic B-splines is used as an approximate function.
Journal ArticleDOI
Soliton solution of some nonlinear partial differential equations and its applications in fluid mechanics
TL;DR: In this paper, an extensive overview of the soliton solutions for some famous partial differential equations like KdV, mKdV and Sine-Gordon is given, and relations between the solitus solution and fluid mechanics are shown.
References
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Journal ArticleDOI
Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
Journal ArticleDOI
The Korteweg-de Vries-Burgers equation
José Canosa,Jenö Gazdag +1 more
TL;DR: The time evolution and stability of the Kortewegde Vries-Burgers equation are studied numerically in this paper, where it is found that nonanalytic initial data satisfying the boundary conditions of the problem evolve asymptotically into the steady-state shocks predicted by a time independent analysis.
Journal ArticleDOI
Galerkin methods applied to some model equations for non-linear dispersive waves
M.E Alexander,J. Ll. Morris +1 more
TL;DR: In this article, the application of a dissipative Galerkin scheme to the numerical solution of the Korteweg de Vries (KdV) and Regularised Long Wave (RLW) equations is investigated.
Journal ArticleDOI
A Hopscotch method for the Korteweg-de-Vries equation
I.S Greig,J. Ll. Morris +1 more
TL;DR: In this paper, a Hopscotch algorithm for the Korteweg-de-Vries equation is presented, which is shown to be conservative and to possess a minimal phase error.
Related Papers (5)
Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves
D. J. de Korteweg,G. de Vries +1 more