Geodesic
Application of the collocation method with B-splines to the GEW equation
Electronic transactions on numerical analysis, Tome 46 (2017), pp. 71-88
In this paper, the generalized equal width (GEW) wave equation is solved numerically by using a quintic B-spline collocation algorithm with two different linearization techniques. Also, a linear stability analysis of the numerical scheme based on the von Neumann method is investigated. The numerical algorithm is applied to three test problems consisting of a single solitary wave, the interaction of two solitary waves, and a Maxwellian initial condition. In order to determine the performance of the numerical method, we compute the error in the $L_{2}$- and $L_{\infty }$- norms and in the invariants $I_1, I_2$, and $I_3$ of the GEW equation. These calculations are compared with earlier studies. Afterwards, the motion of solitary waves according to different parameters is designed.
Classification : 41A15, 65N30, 76B25
Keywords: GEW equation, finite element method, quintic B-spline, soliton, solitary waves 
@article{ETNA_2017__46__a9,
     author = {Zeybek,  Halil and Gazi Karako\c{c},  S.Battal},
     title = {Application of the collocation method with {B-splines} to the {GEW} equation},
     journal = {Electronic transactions on numerical analysis},
     pages = {71--88},
     year = {2017},
     volume = {46},
     zbl = {1357.76058},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2017__46__a9/}
}
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Zeybek,  Halil; Gazi Karakoç,  S.Battal. Application of the collocation method with B-splines to the GEW equation. Electronic transactions on numerical analysis, Tome 46 (2017), pp. 71-88. http://geodesic.mathdoc.fr/item/ETNA_2017__46__a9/