 # WSEAS Transactions on Mathematics

Print ISSN: 1109-2769
E-ISSN: 2224-2880

Volume 17, 2018

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.

Volume 17, 2018

Numerical Solution of Quadratic General Korteweg-De Vries Equation by Galerkin Quadratic Finite Element Method

AUTHORS: Meknani Bassem, Messaoudi Rima, Talaat Abdelhamid, Nasserdine Kechkar, Ehab S. Selima

ABSTRACT: In this work, we consider the quadratic generalized Kortewegde Vries (QGKdV) equation that is a mathematical model of waves on shallow water surfaces. Numerical solution of a Cauchy boundary-value problem with known exact solution is developed in details. Discretization is first accomplished by means of a quadratic finite element method. Then, the obtained system of first-order ordinary differential equations is discretized through a backward finite difference formula. Finally, the derived non linear algebraic system is solved by Newton’s method with the Gauss elimination method as the inner iteration solver. Numerical results are presented in order to illustrate the efficiency of the present numerical treatment. In addition, a general form of multiple-soliton solution of QGKdV equation is obtained using the simplest equation method with Burgers equation as simplest equation

KEYWORDS: KdV equation, Finite element method, Finite difference method.

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WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 17, 2018, Art. #28, pp. 220-228 