Unconditional optimal error estimates of conservative methods for Klein–Gordon–Dirac system in two dimensions.

In this work, we propose and analyze finite difference methods for solving two-dimensional Klein–Gordon–Dirac (KGD) system. Due to the nonlinear coupling, it is a great challenge to design and analyze numerical methods for KGD system. To overcome this difficulty, two linearized, decoupled and conservative finite difference methods are presented, which are mass- and energy-conserved. By rigorous error estimates, the conservative methods converge with second-order accuracy in both spatial and temporal discretizations without any requirements on the grid ratios. Several numerical experiments are carried out to illustrate the performance of the proposed numerical methods. [ABSTRACT FROM AUTHOR]