Abstract and Applied Analysis

A Numerical Solution for Hirota-Satsuma Coupled KdV Equation

M. S. Ismail and H. A. Ashi

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Abstract

A Petrov-Galerkin method and product approximation technique are used to solve numerically the Hirota-Satsuma coupled Korteweg-de Vries equation, using cubic B -splines as test functions and a linear B -spline as trial functions. The implicit midpoint rule is used to advance the solution in time. Newton’s method is used to solve the block nonlinear pentadiagonal system we have obtained. The resulting schemes are of second order accuracy in both directions, space and time. The von Neumann stability analysis of the schemes shows that the two schemes are unconditionally stable. The single soliton solution and the conserved quantities are used to assess the accuracy and to show the robustness of the schemes. The interaction of two solitons, three solitons, and birth of solitons is also discussed.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 819367, 9 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412277159

Digital Object Identifier
doi:10.1155/2014/819367

Mathematical Reviews number (MathSciNet)
MR3253585

Zentralblatt MATH identifier
07023139

Citation

Ismail, M. S.; Ashi, H. A. A Numerical Solution for Hirota-Satsuma Coupled KdV Equation. Abstr. Appl. Anal. 2014 (2014), Article ID 819367, 9 pages. doi:10.1155/2014/819367. https://projecteuclid.org/euclid.aaa/1412277159


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