3 papers
math.AP2022
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…
math.NA2019
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…
math.DS2017
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…