Numerical analysis of a new conservative scheme for the 2D generalized Rosenau-RLW equation

Abstract

In this paper, a conservative finite difference scheme to solve the generalized Rosenau-RLW equation in 2D is proposed. The proposed scheme is linear-implicit, mass-preserving, energy-preserving, uniquely solvable, unconditionally stable, and its numerical convergence is of second order in the $l_{\mathrm{\infty }}$-norm. Results from numerical experiments are reported to demonstrate that the scheme is accurate, efficient and reliable.

Keywords:

• Rosenau-RLW equation
• uniqueness
• convergence
• unconditional stability

2010 Mathematics Subject Classifications:

• 65M12
• 65N06

Disclosure statement

No potential conflict of interest was reported by the authors.