Two efficient methods for solving the generalized regularized long wave equation

ABSTRACT

In this paper, an exact method named Riccati–Bernoulli sub-ODE method and a numerical method named Subdomain finite element method are proposed for solving the nonlinear generalized regularized long wave (GRLW) equation. For this purpose, Bäcklund transformation of the Riccati–Bernoulli equation and sextic B-spline functions are used for the exact and numerical solutions, respectively. The single soliton wave motion is used to confirm the methods which are found to be correct and effective. The three invariants ($I_1$, $I_2$ and $I_3$) of motion have been assessed to indicate the conservation properties of the numerical algorithm. For the motion of single solitary $L_2$ and $L_{\mathrm{\infty }}$ error norms are handled to evaluate differences between the analytical and numerical solutions. Unconditional stability is demonstrated using von-Neumann method. The procured outcomes show that our new schemes guarantee an evident and a functional mathematical equipment for solving nonlinear evolution equations.

Keywords:

• GRLW equation
• subdomain
• Riccati–Bernoulli sub-ODE method
• Bäcklund transformation
• sextic B-splines
• solitary waves

AMS Classifications:

• 65N30
• 65D07
• 74S05
• 74J35
• 76B25

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The project is supported by NSF of China (11371289, 11501441).