NUMERICAL STUDIES ON THE KLEIN-GORDON-SCHRODINGER EQUATIONS IN THE SINGULAR LIMIT REGIME

Abstract

Klein-Gordon-Schrodinger (KGS) equations describes a system of a conserved scalar nucleon interacting with a neutral scalar meson coupled through the Yukawa interaction. In this thesis, I proposed some exciting numerical methods for the KGS equations with periodic boundary conditions and three types of initial data, i.e., the well-prepared, ill-prepared and extremely ill-prepared initial data in the first part. Error estimate of the finite difference methods are given for the classical regime. In the second part, we tackled the numerical methods for the KGS equations in the singular limit regime, of which the solutions have high oscillation in time. We proposed two uniform convergence methods for the KGS equations, which are based on the exponential wave integrator and time-splitting Fourier pseudospectral methods. Some improvement are given based on the multi-scale analysis of the KGS equations. Extensive numerical results are reported to demonstrate the efficiency, accuracy and scalability of all the methods.