Linearly implicit conservative schemes for long-term numerical simulation of Klein–Gordon–Schrödinger equations

In this paper, we propose three linearly implicit Fourier pseudospectral algorithms for solving the Klein–Gordon–Schrödinger equations in quantum physics. All methods are linearly implicit in the sense that they do not need iterative technique to solve nonlinear equations at each time step. The three algorithms are proved to admit the charge and energy conservation laws exactly. Numerical results reveal that all the proposed methods can provide accurate soliton solutions and simulate the collision of solitons well. The numerical results also verify the theoretical analysis that the proposed methods are all charge-preserving and energy-preserving algorithms.