Unconditionally stable solution for wave equations of the second order

This paper reports an unconditionally stable and implicit method to solve the electromagnetic wave equations of the second order numerically without the Courant limit. By using the Crank-Nicolson (CN) scheme with the Douglas-Gunn (DG) algorithm, the numerical solution is second order accurate in both space and time. Two schemes are introduced and compared, and the numerical dispersion relations are given. Numerical experiments agree with the numerical dispersion predicted in theory.