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

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

5 The Maxwell-Klein-Gordon equation describes the interaction of a charged particle with 6 an electromagnetic field. Solving this equation in the non-relativistic limit regime, i.e. 7 the speed of light c formally tending to infinity, is numerically very delicate as the so8 lution becomes highly-oscillatory in time. In order to resolve the oscillations, standard 9 numerical time integration sch...

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.

Uniformly accurate numerical schemes for highly oscillatory Klein-Gordon and nonlinear Schrödinger equations

This work is devoted to the numerical simulation of nonlinear Schrödinger and Klein-Gordon equations. We present a general strategy to construct numerical schemes which are uniformly accurate with respect to the oscillation frequency. This is a stronger feature than the usual so called “Asymptotic preserving” property, the last being also satisfied by our scheme in the highly oscillatory limit....

B-SPLINE COLLOCATION APPROACH FOR SOLUTION OF KLEIN-GORDON EQUATION

We develope a numerical method based on B-spline collocation method to solve linear Klein-Gordon equation. The proposed scheme is unconditionally stable. The results of numerical experiments have been compared with the exact solution to show the efficiency of the method computationally. Easy and economical implementation is the strength of this approach.  

WAVELET SOLUTIONS OF THE KLEIN-GORDON EQUATION