Finite difference approximations for the modified equal width wave (MEW) equation

Abstract

In this paper, the modified equal width wave (MEW) equation is solved numerically using the finite difference method. The stability analysis using Von-Neumann technique shows the schemes are unconditionally stable. Also the local truncation error of the method is investigated. Three invariant of motion are evaluated to determine the conservation properties of the problem, and the numerical scheme leads to accurate and efficient results. Moreover, interaction two and three solitary waves are studied. The development of the Maxwellian initial condition into solitary waves is also shown, and we shown that the number of solitons which are generated from the Maxwellian initial condition can be determined.