Convergence analysis of Runge-Kutta multiresolution time-domain scheme

The MRTD method highlighted an improvement in the observed dispersion characteristics over the classical FDTD, however the high convergence is hindered because of the low order time-stepping procedure. In this paper, we analyze the convergence of a newly introduced scheme in which the MRTD is incorporated a high-order Runge-Kutta time integrators technique, and show that the mth-order convergence can only be achieved using the same spatial integration order and the same mth-order SSP RK method.