Tbilisi Mathematical Journal

A Lumped Galerkin finite element method for the generalized Hirota-Satsuma coupled KdV and coupled MKdV equations

Nuri Murat Yagmurlu, Berat Karaagac, and Alaattin Esen

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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.

Article information

Source
Tbilisi Math. J., Volume 12, Issue 3 (2019), 159-173.

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

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1569463241

Digital Object Identifier
doi:10.32513/tbilisi/1569463241

Mathematical Reviews number (MathSciNet)
MR4012390

Subjects
Primary: 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Secondary: 65D07: Splines 65L06: Multistep, Runge-Kutta and extrapolation methods 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]

Keywords
the generalized Hirota-Satsuma coupled KdV and coupled mKdV finite element method Galerkin method B-spline Runge-Kutta

Citation

Yagmurlu, Nuri Murat; Karaagac, Berat; Esen, Alaattin. A Lumped Galerkin finite element method for the generalized Hirota-Satsuma coupled KdV and coupled MKdV equations. Tbilisi Math. J. 12 (2019), no. 3, 159--173. doi:10.32513/tbilisi/1569463241. https://projecteuclid.org/euclid.tbilisi/1569463241


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