Convergence analysis of the higher-order global mass-preserving numerical method for the symmetric regularized long-wave equation

Abstract

A higher-order uncoupled finite difference scheme is proposed and analysed to approximate the solutions of the symmetric regularized long-wave equation. The finite difference technique preserving the global conservation laws precisely on any time-space regions gives a three-level linear-implicit scheme with a tridiagonal system. The existence and uniqueness of numerical solutions are guaranteed while the convergence and stability are verified. In addition, the error estimation in $\parallel \cdot {\parallel }_{\mathrm{\infty }}$-norm for the proposed scheme is examined, and the spatial accuracy is analysed and found to be fourth order on a uniform grid. The scheme is also proved to conserve mass and bound of solutions. Some numerical tests are presented to illustrate the theoretical results and the efficiency of the scheme. The consequences confirm that the proposed scheme gives an improvement over existing schemes. Moreover, in the numerical simulations, the faithfulness of the proposed method is validated by the evidences of an overtaking collision between two elevation solitary waves and a head-on collision between elevation as well as depression solitary waves under the effect of variable parameters.

Keywords:

• SRLW equation
• higher-order finite difference method
• convergence
• stability

2010 Mathematics Subject Classification:

• 65M06

Disclosure statement

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

Additional information

Funding

This research was supported by the Centre of Excellence in Mathematics, the Commission on Higher Education and Chiang Mai University.