Eur. Phys. J. Plus (2019) 134: 367
https://doi.org/10.1140/epjp/i2019-12748-1

Regular Article

Solitary wave solution of the nonlinear KdV-Benjamin-Bona-Mahony-Burgers model via two meshless methods

School of Mathematics, Iran university of Science and Technology, Narmak, 16846-13114, Tehran, Iran

^* e-mail: golbabai@iust.ac.ir

Received: 21 January 2019
Accepted: 9 May 2019
Published online: 30 July 2019

Abstract

A nonlinear wave phenomenon is one of the significant fields of scientific research, which a lot of researchers in the past have deliberated about mathematical models clarifying the treatment. The nonlinear Korteweg-de Vries-Benjamin-Bona-Mahony-Burgers (KdV-BBM-B) model plays an essential role in numerous subjects of engineering and science. This model is numerically approximated by means of the combination of the radial basis function (RBF) and the finite difference (RBF-FD), RBF-pseudospectral (RBF-PS) that are stated in this paper. These methods are meshless, and no obligation is required to linearize the nonlinear parts. The radial kernels are employed to convert the PDE into a system of ODEs. This ODE system is solved with the help of the higher-order ODE solver. In addition, it is indicated that the present numerical techniques are stable. To evaluate the validity and applicability of the aforesaid techniques, the error norms and three invariants I₁, I₂ and I₃ are calculated and displayed both numerically and graphically. The obtained results are compared with previous schemes found in the literature.