A convergent two-level linear scheme for the generalized Rosenau–KdV–RLW equation
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Date
2019
Authors
Aydın, Ayhan
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Publisher
Tubitak Scientific & Technological Research Council Turkey
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Abstract
A new convergent two-level finite difference scheme is proposed for the numerical solution of initial valueproblem of the generalized Rosenau–KdV–RLW equation. The new scheme is second-order, linear, conservative, andunconditionally stable. It contains one free parameter. The impact of the parameter to error of the numerical solutionis studied. The prior estimate of the finite difference solution is obtained. The existence, uniqueness, and convergence ofthe scheme are proved by the discrete energy method. Accuracy and reliability of the scheme are tested by simulating thesolitary wave graph of the equation. Wave generation subject to initial Gaussian condition has been studied numerically.Different wave generations are observed depending on the dispersion coefficients and the nonlinear advection term.Numerical experiments indicate that the present scheme is conservative, efficient, and of high accuracy, and well simulatesthe solitary waves for a long time.
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Aydin, Ayhan/0000-0002-0837-9364
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Keywords
Matematik
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0
WoS Q
Q2
Scopus Q
Q2
Source
Turkish Journal of Mathematics
Volume
43
Issue
5
Start Page
2226
End Page
2245