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July 2019 A Lumped Galerkin finite element method for the generalized Hirota-Satsuma coupled KdV and coupled MKdV equations
Nuri Murat Yagmurlu, Berat Karaagac, Alaattin Esen
Tbilisi Math. J. 12(3): 159-173 (July 2019). DOI: 10.32513/tbilisi/1569463241

Abstract

In the present study, a Lumped Galerkin finite element method using quadratic B-splines has been applied to the generalized Hirota-Satsuma coupled Korteweg de Vries (KdV) and coupled modified Korteweg-de Vries (mKdV) equations. The numerical solutions of discretized equations using Lumped Galerkin finite element method have been obtained using the fourth order Runge-Kutta method which is widely used for the solution of ordinary differential equation system. The numerical solutions obtained for various space and time values have been compared with exact ones using the error norms $L_{2}$ and $L_{\infty}$. Lumped Galerkin finite element method is an effective one which can be applied to a wide range of nonlinear evolution equations.

Citation

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Nuri Murat Yagmurlu. Berat Karaagac. Alaattin Esen. "A Lumped Galerkin finite element method for the generalized Hirota-Satsuma coupled KdV and coupled MKdV equations." Tbilisi Math. J. 12 (3) 159 - 173, July 2019. https://doi.org/10.32513/tbilisi/1569463241

Information

Received: 7 May 2018; Accepted: 10 August 2019; Published: July 2019
First available in Project Euclid: 26 September 2019

zbMATH: 07172332
MathSciNet: MR4012390
Digital Object Identifier: 10.32513/tbilisi/1569463241

Subjects:
Primary: 65N30
Secondary: 35Q53, 65D07, 65L06

Rights: Copyright © 2019 Tbilisi Centre for Mathematical Sciences

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Vol.12 • No. 3 • July 2019
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