A collocation algorithm based on quintic B-splines for the solitary wave simulation of the GRLW equation

Document Type : Research Note


1 Department of Applied Mathematics, Faculty of Computer Science, Abdullah G¨ul University, 38080 Kayseri, Turkey

2 Department of Mathematics, Faculty of Science and Art, Nevs¸ehir Hacı Bektas¸ Veli University, 50300 Nevs¸ehir, Turkey


In this article, a collocation algorithm based on quintic B-splines is proposed for the numerical solution of the non-linear generalized regularized long wave (GRLW) equation. Also, to analyse the linear stability of the numerical scheme, the von-Neumann technique is used. The numerical approach is discussed on three test examples consisting of a single solitary wave, the collision of two solitary waves and the growth of an undular bore. The accuracy of the method is demonstrated by calculating the error in the L2 and L¥ norms and the conservative quantities I1, I2 and I3. The findings are compared with those of previously reported in the literature. Finally, the motion of solitary waves is graphically plotted according to different parameters.


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