A Second Order Symplectic Partitioned Runge-Kutta Scheme for Maxwell's Equations

摘要

We construct a new scheme for approximating the solution to infinite dimensional non-separable Hamiltonian systems of Maxwell's equations using a second order symplectic partitioned Runge-Kutta (PRK) method for the first time. The scheme is obtained by discretizing the Maxwell's equations in the time direction based on symplectic PRK method, and then evaluating the equation in the spatial direction with a suitable finite difference approximation. Also numerical examples are presented to verify the efficiency of the scheme.