TY - JOUR
T1 - Eventual periodicity of the forced oscillations for a Korteweg–de Vries type equation on a bounded domain using a sinc collocation method
AU - Al-Khaled, Kamel
AU - Haynes, Nicholas
AU - Schiesser, William
AU - Usman, Muhammad
N1 - Publisher Copyright:
© 2017 Elsevier B.V.
PY - 2018/3/1
Y1 - 2018/3/1
N2 - We demonstrate numerically the eventual time periodicity of solutions u(.,t) to the Korteweg–de Vries type equation with periodic forcing at one end using the sinc-collocation method. This method approximates the space dimension of the solution with a cardinal expansion of sinc functions, thus allowing the avoidance of a costly finite difference grid for a third order boundary value problem. The first order time derivative is approximated with a θ-weighted finite difference method. The sinc-collocation method was found to be more robust and more efficient than other numerical schemes when applied to this problem.
AB - We demonstrate numerically the eventual time periodicity of solutions u(.,t) to the Korteweg–de Vries type equation with periodic forcing at one end using the sinc-collocation method. This method approximates the space dimension of the solution with a cardinal expansion of sinc functions, thus allowing the avoidance of a costly finite difference grid for a third order boundary value problem. The first order time derivative is approximated with a θ-weighted finite difference method. The sinc-collocation method was found to be more robust and more efficient than other numerical schemes when applied to this problem.
KW - Eventual periodicity
KW - KdV equation
KW - Sinc collocation method
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U2 - 10.1016/j.cam.2017.08.023
DO - 10.1016/j.cam.2017.08.023
M3 - Article
AN - SCOPUS:85030480828
SN - 0377-0427
VL - 330
SP - 417
EP - 428
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
ER -