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July 2019 Operator splitting method for numerical solution of modified equal width equation
İhsan Çelikkaya
Tbilisi Math. J. 12(3): 51-67 (July 2019). DOI: 10.32513/tbilisi/1569463234

Abstract

In this manuscript, numerical solutions of the equations in the form of $u_{t}=Au+B(u)$ have been sought for, where $A$ and $B$ are linear and nonlinear operators, respectively. The modified equal width (MEW) equation has been converted into two sub problems. Then, the sub problems were solved according to the Strang splitting scheme by applying the cubic B-spline collocation finite element method. Thus, more accurate results of the equation MEW have been obtained than those non-splitting users. In order to test the accuracy and efficiency of the present method; single soliton, interaction of two solitons and Maxwellian initial condition pulse problems have been considered. Moreover, the stability analysis of each sub problem has been investigated by von-Neumann analysis method.

Citation

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İhsan Çelikkaya. "Operator splitting method for numerical solution of modified equal width equation." Tbilisi Math. J. 12 (3) 51 - 67, July 2019. https://doi.org/10.32513/tbilisi/1569463234

Information

Received: 24 May 2018; Accepted: 25 June 2019; Published: July 2019
First available in Project Euclid: 26 September 2019

zbMATH: 07172325
MathSciNet: MR4012383
Digital Object Identifier: 10.32513/tbilisi/1569463234

Subjects:
Primary: 35Q51
Secondary: 33F10, 74J35

Rights: Copyright © 2019 Tbilisi Centre for Mathematical Sciences

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Vol.12 • No. 3 • July 2019
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