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An adaptive method of lines solution of the Korteweg-de Vries equation

โœ Scribed by P. Saucez; A.Vande Wouwer; W.E. Schiesser

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
965 KB
Volume
35
Category
Article
ISSN
0898-1221

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โœฆ Synopsis

Following a method of lines formulation, the Korteweg-deVries equation is solved using a static spatial remeshing algorithm based on the equidistribution principle, which allows the number of nodes to be significantly reduced as compared to a fixed-grid solution.

Several finite difference schemes, including direct and stagewise procedures, are compared and the results of a large number of computational experiments are presented, which demonstrate that the selection of a spatial approximation scheme for the third-order derivative term is the primary determinant of solution accuracy.

๐Ÿ“œ SIMILAR VOLUMES

An exact solution of the Korteweg-de Vri
An exact solution of the Korteweg-de Vries equation with dissipation
โœ M. W. Kalinowski; M. Grundland ๐Ÿ“‚ Article ๐Ÿ“… 1981 ๐Ÿ› Springer ๐ŸŒ English โš– 160 KB

By means of the method proposed in the papers [1,2] we look for solutions of the Korteweg-de Vries equation with dissipation. A new solution is found and expressed by means of the Weierstrass ~-function.

Numerical solution of the Korteweg-de Vr
Numerical solution of the Korteweg-de Vries (KdV) equation
โœ P.C. Jain; Rama Shankar; Dheeraj Bhardwaj ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 459 KB

numerical method is developed for solving the Korteweg-de Vries (KdV) equation u, -6uu, f u xxx = 0 by using splitting method and quintic spline approximation technique. The convergence, stability and accuracy of the proposed method are discussed. Further, the method is extended to solve the perturb