Different efficient and accurate numerical methods have recently been proposed and
analyzed for the nonlinear Klein-Gordon equation (NKGE) with a dimensionless parameter …

In this paper, we consider a class of highly oscillatory Hamiltonian systems which involve a
scaling parameter. The problem arises from many physical models in some limit parameter …

In this paper, we consider the three dimensional Vlasov equation with an inhomogeneous,
varying direction, strong magnetic field. Whenever the magnetic field has constant intensity …

In this paper we address the computational aspects of uniformly accurate numerical
methods for solving highly oscillatory evolution equations. In particular, we introduce an …

We establish uniform error bounds of an exponential wave integrator Fourier pseudospectral
(EWI-FP) method for the long-time dynamics of the nonlinear Klein--Gordon equation …

Many hyperbolic and kinetic equations contain a non-stiff convection/transport part and a stiff
relaxation/collision part (characterized by the relaxation or mean free time $\varepsilon $) …

In this paper we propose a numerical method to solve a 2D advection-diffusion equation, in
the highly oscillatory regime. We use an efficient and robust integrator which leads to an …

We consider a kind of differential equations y˙(t)= R (y (t)) y (t)+ f (y (t)) with energy
conservation. Such conservative models appear for instance in quantum physics …

In this work, we consider the numerical solution of the nonlinear Schrödinger equation with a
highly oscillatory potential (NLSE-OP). The NLSE-OP is a model problem which frequently …

This work concerns the time averaging techniques for the nonlinear Klein-Gordon (KG)
equation in the nonrelativistic limit regime which have recently gained a lot of attention in …