Abstract and Applied Analysis

Petrov-Galerkin Method for the Coupled Schrödinger-KdV Equation

M. S. Ismail, Farida M. Mosally, and Khadeejah M. Alamoudi

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Abstract

Petrov-Galerkin method is used to derive a numerical scheme for the coupled Schrödinger-KdV (SKdV) equations, where we have used the cubic B-splines as a test functions and a linear B-splines as a trial functions. Product approximation technique is used to deal with the nonlinear terms. An implicit midpoint rule and the Runge-Kutta method of fourth-order (RK4) are used to discretize in time. A block nonlinear pentadiagonal system is obtained. We solve this system by the fixed point method. The resulting scheme has a fourth-order accuracy in space direction and second-order in time direction in case of the implicit midpoint rule and it is unconditionally stable by von Neumann method. Using the RK4 method the scheme will be linear and fourth-order in time and space directions, and it is also conditionally stable. The exact soliton solution and the conserved quantities are used to assess the accuracy and to show the robustness and the efficiency of the proposed schemes.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 705204, 8 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412277049

Digital Object Identifier
doi:10.1155/2014/705204

Mathematical Reviews number (MathSciNet)
MR3226222

Zentralblatt MATH identifier
07022911

Citation

Ismail, M. S.; Mosally, Farida M.; Alamoudi, Khadeejah M. Petrov-Galerkin Method for the Coupled Schrödinger-KdV Equation. Abstr. Appl. Anal. 2014 (2014), Article ID 705204, 8 pages. doi:10.1155/2014/705204. https://projecteuclid.org/euclid.aaa/1412277049


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