Petrov-Galerkin Method for the Coupled Schrödinger-KdV Equation
Joint Authors
Mosally, Farida
Alamoudi, Khadeejah M.
Ismail, M. S.
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-06-15
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Ismail, M. S.& Mosally, Farida& Alamoudi, Khadeejah M.. 2014. Petrov-Galerkin Method for the Coupled Schrödinger-KdV Equation. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-8.
https://search.emarefa.net/detail/BIM-1033948
Modern Language Association (MLA)
Ismail, M. S.…[et al.]. Petrov-Galerkin Method for the Coupled Schrödinger-KdV Equation. Abstract and Applied Analysis No. 2014 (2014), pp.1-8.
https://search.emarefa.net/detail/BIM-1033948
American Medical Association (AMA)
Ismail, M. S.& Mosally, Farida& Alamoudi, Khadeejah M.. Petrov-Galerkin Method for the Coupled Schrödinger-KdV Equation. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-8.
https://search.emarefa.net/detail/BIM-1033948
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1033948