Efficient time integration of the Maxwell-Klein-Gordon equation in the non-relativistic limit regime

Applications of He’s Variational Principle method and the Kudryashov method to nonlinear time-fractional differential equations

  In this paper, we establish exact solutions for the time-fractional Klein-Gordon equation, and the time-fractional Hirota-Satsuma coupled KdV system. The He’s semi-inverse and the Kudryashov methods are used to construct exact solutions of these equations. We apply He’s semi-inverse method to establish a variational theory for the time-fractional Klein-Gordon equation, and the time-fractiona...

Analytical solutions for the fractional Klein-Gordon equation

In this paper, we solve a inhomogeneous fractional Klein-Gordon equation by the method of separating variables. We apply the method for three boundary conditions, contain Dirichlet, Neumann, and Robin boundary conditions, and solve some examples to illustrate the effectiveness of the method.

Asymptotic preserving schemes for the Klein-Gordon equation in the non-relativistic limit regime

— We consider the Klein-Gordon equation in the non-relativistic limit regime, i.e. the speed of light c tending to infinity. We construct an asymptotic expansion for the solution with respect to the small parameter depending on the inverse of the square of the speed of light. As the first terms of this asymptotic can easily be simulated our approach allows us to construct numerical algorithms t...

Non-relativistic limit of Klein-Gordon Maxwell

We deal with the derivation of the Schrödinger-Poisson system as a non-relativistic limit (i.e. c→∞ where c is the speed of light) of the Klein-GordonMaxwell or the Dirac-Maxwell system on R. We deal with convergence in the energy space C([0, T ];H). We use and motivate a splitting of the scalar Klein-Gordon field into a sum of two fields, corresponding, in the physical interpretation, to elect...

WAVELET SOLUTIONS OF THE KLEIN-GORDON EQUATION