7 papers
On estimates for a class of strongly damped wave equations
Haidar Mohamad
The purpose of this paper is to obtain a fundamental estimate for a class of a strongly damped wave equations where the damping operator is given by with $δ\geq…
Quasi-convergence of an implementation of optimal balance by backward-forward nudging
G. Tuba Masur, Haidar Mohamad, Marcel Oliver
Optimal balance is a non-asymptotic numerical method to compute a point on the slow manifold for certain two-scale dynamical systems. It works by solving a modified version of the…
Energy asymptotics for the strongly damped Klein-Gordon equation
Haidar Mohamad
We consider the strongly damped Klein Gordon equation for defocusing nonlinearity and we study the asymptotic behaviour of the energy for periodic solutions. We prove first the exp…
High-order uniformly accurate time integrators for semilinear wave equations of Klein-Gordon type in the non-relativistic limit
Haidar Mohamad, Marcel Oliver
We introduce a family of high-order time semi-discretizations for semilinear wave equations of Klein--Gordon type with arbitrary smooth nonlinerities that are uniformly accurate in…
Numerical integration of functions of a rapidly rotating phase
Haidar Mohamad, Marcel Oliver
We present an algorithm for the efficient numerical evaluation of integrals of the form \[ I(ω) = \int_0^1 F( x,\mathrm e^{\mathrm i ωx}; ω) \, \mathrm d x \] for sufficiently smoo…
Optimal balance via adiabatic invariance of approximate slow manifolds
Georg A. Gottwald, Haidar Mohamad, Marcel Oliver
We analyze the method of optimal balance which was introduced by Viudez and Dritschel (J. Fluid Mech. 521, 2004, pp. 343-352) to provide balanced initializations for two-dimensiona…
Some existence results for the modified binormal curvature flow equation
Haidar Mohamad
We establish existence and uniqueness results for the modified binormal curvature flow equation that generalizes the binormal curvature flow equation for a curve in In this…