We study the initial-boundary problem of dissipative symmetric regularized long wave equations with damping term. Crank-Nicolson nonlinear-implicit finite difference scheme is designed. Existence and uniqueness of numerical solutions are derived. It is proved that the finite difference scheme is of second-order convergence and unconditionally stable by the discrete energy method. Numerical simu...

Analytical and numerical simulations are carried out in order to identify physical parameters affecting acoustic and motion control by viscoelastic piezo-electric and material damping. Numerical simulations in terms of critical parameters, such as relaxation functions of the structure and piezo-electric devices, aerodynamic coefficients, Mach number, are carried out to evaluate their sensitivit...

The low-rank damping term appears commonly in quadratic eigenvalue problems arising from physical simulations. To exploit the low-rank damping property, we propose a Padé Approximate Linearization (PAL) algorithm. The advantage of the PAL algorithm is that the dimension of the resulting linear eigenvalue problem is only n+ lm, which is generally substantially smaller than the dimension 2n of th...

Nonlinear long wave propagation in a medium with periodic parameters is considered in the framework of a variable-coefficient Korteweg-de Vries equation. The characteristic period of the variable medium is varied from slow to rapid, and its amplitude is also varied. For the case of a piecewise constant coefficient with a large scale for each constant piece, explicit results for the damping of a...

We investigate blow-up of the focusing nonlinear Schrödinger equation, in the critical and supercritical cases. Numerical simulations are performed to examine the dependence of the time at which blow-up occurs on properties of the data or the equation. Three cases are considered: dependence on the scale of the nonlinearity when the initial data are fixed; dependence upon the strength of a quadr...

Introduction: In the absence of energy dissipation, obliquity variations of Mars would likely be chaotic. However, relatively small amounts of dissipation suffice to suppress the chaotic variations. Tidal dissipation within Mars, as constrained by the observed evolution of the orbit of Phobos, appears sufficient to regularize the obliquity variations. If Mars has a fluid core, viscous core-mant...