A second order symplectic partitioned Runge-Kutta scheme for Maxwell´s equations

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.