Numerical solution of the Yukawa-coupled Klein–Gordon–Schrödinger equations via a Chebyshev pseudospectral multidomain method

The Klein–Gordon–Schrödinger equations describe a classical model of the interaction between conservative complex neutron field and neutral meson Yukawa in quantum field theory. In this paper, we study the long-time behavior of solutions for the Klein–Gordon–Schrödinger equations. We propose the Chebyshev pseudospectral collocation method for the approximation in the spatial variable and the explicit Runge–Kutta method in time discretization. In comparison with the single domain, the domain decomposition methods have good spatial localization and generate a sparse space differentiation matrix with high accuracy. In this study, we choose an overlapping multidomain scheme. The obtained numerical results show the Pseudospectral multidomain method has excellent long-time numerical behavior and illustrate the effectiveness of the numerical scheme in controlling two particles. Some comparisons with single domain pseudospectral and finite difference methods will be also investigated to confirm the efficiency of the new procedure.