Abstract
The current article considers the sextic B-spline collocation methods (SBCM1 and SBCM2) to approximate the solution of the modified regularized long wave ( MRLW ) equation. In view of this, we will study the solitary wave motion and interaction of higher (two and three) solitary waves. Also, the modified Maxwellian initial condition into solitary waves is studied. Moreover, the stability analysis of the methods has been discussed, and these will be unconditionally stable. Moreover, we have calculated the numerical conserved laws and error norms L 2 and L ∞ to demonstrate the efficiency and accuracy of the method. The numerical examples are presented to illustrate the applications of the methods and to compare the computed results with the other methods. The results show that our proposed methods are more accurate than the other methods.
Highlights
The regularized long wave (RLW) equation is defined by the following nonlinear partial differential equation [1]: στ + ση + ζσση − μσηητ = 0, ð1Þ
The numerical solutions of the RLW equation has been studied by many researchers via various methods, such as finite difference methods [4, 5], Fourier pseudospectral methods [6], various models of finite element methods including least square, collocation, and Galerkin methods [7,8,9], mesh-free method [10], and Galerkin finite element methods [11,12,13]
The generalized form of the RLW equation is known as the GMRLW equation which is given by στ + ση + ζσpση − μσηητ = 0, ð2Þ
Summary
The regularized long wave (RLW) equation is defined by the following nonlinear partial differential equation [1]: στ + ση + ζσση − μσηητ = 0, ð1Þ where μ and ζ are positive parameters. This equation was first introduced by Peregrine [1] and after that by Benjamin et al [2] to describe the behavior of the undular bore. There are many analytical methods to obtain the solution of the RLW equation for certain boundary and initial conditions; for example, see [2, 3].
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