A Taylor-Galerkin finite element method for the KdV equation using cubic B-splines

Aynur Canvar; Murat Sari; Idris Dag

doi:10.1016/j.physb.2010.05.008

A Taylor-Galerkin finite element method for the KdV equation using cubic B-splines

Aynur Canvar, Murat Sari^*, Idris Dag

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

22 Citations (Scopus)

Abstract

In this paper, to obtain accurate solutions of the Kortewegde Vries (KdV) equation, a TaylorGalerkin method is proposed based on cubic B-splines over finite elements. To tackle this a forward time-stepping technique is accepted in time. To see the accuracy of the proposed method, L₂ and L∞ error norms are calculated in three test problems. The numerical results are found to be in good agreement with exact solutions and with the literature. The applied numerical method has also been shown to be unconditionally stable. In order to find out the physical behaviour of more intricate models, this procedure has been seen to have a great potentiality.

Original language	English
Pages (from-to)	3376-3383
Number of pages	8
Journal	Physica B: Condensed Matter
Volume	405
Issue number	16
DOIs	https://doi.org/10.1016/j.physb.2010.05.008
Publication status	Published - 15 Aug 2010
Externally published	Yes

Keywords

Cubic B-splines
KdV equation
Partial differential equations
Soliton
TaylorGalerkin finite element method

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10.1016/j.physb.2010.05.008

Cite this

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title = "A Taylor-Galerkin finite element method for the KdV equation using cubic B-splines",

abstract = "In this paper, to obtain accurate solutions of the Kortewegde Vries (KdV) equation, a TaylorGalerkin method is proposed based on cubic B-splines over finite elements. To tackle this a forward time-stepping technique is accepted in time. To see the accuracy of the proposed method, L2 and L∞ error norms are calculated in three test problems. The numerical results are found to be in good agreement with exact solutions and with the literature. The applied numerical method has also been shown to be unconditionally stable. In order to find out the physical behaviour of more intricate models, this procedure has been seen to have a great potentiality.",

keywords = "Cubic B-splines, KdV equation, Partial differential equations, Soliton, TaylorGalerkin finite element method",

author = "Aynur Canvar and Murat Sari and Idris Dag",

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AU - Canvar, Aynur

AU - Sari, Murat

AU - Dag, Idris

PY - 2010/8/15

Y1 - 2010/8/15

N2 - In this paper, to obtain accurate solutions of the Kortewegde Vries (KdV) equation, a TaylorGalerkin method is proposed based on cubic B-splines over finite elements. To tackle this a forward time-stepping technique is accepted in time. To see the accuracy of the proposed method, L2 and L∞ error norms are calculated in three test problems. The numerical results are found to be in good agreement with exact solutions and with the literature. The applied numerical method has also been shown to be unconditionally stable. In order to find out the physical behaviour of more intricate models, this procedure has been seen to have a great potentiality.

AB - In this paper, to obtain accurate solutions of the Kortewegde Vries (KdV) equation, a TaylorGalerkin method is proposed based on cubic B-splines over finite elements. To tackle this a forward time-stepping technique is accepted in time. To see the accuracy of the proposed method, L2 and L∞ error norms are calculated in three test problems. The numerical results are found to be in good agreement with exact solutions and with the literature. The applied numerical method has also been shown to be unconditionally stable. In order to find out the physical behaviour of more intricate models, this procedure has been seen to have a great potentiality.

KW - Cubic B-splines

KW - KdV equation

KW - Partial differential equations

KW - Soliton

KW - TaylorGalerkin finite element method

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SN - 0921-4526

VL - 405

SP - 3376

EP - 3383

JO - Physica B: Condensed Matter

JF - Physica B: Condensed Matter

IS - 16

ER -

A Taylor-Galerkin finite element method for the KdV equation using cubic B-splines

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Keywords

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