Study and analysis of a novel Runge-Kutta high-order finite-difference time-domain method

In this study, a novel high-order finite-difference time-domain (HO-FDTD) method, Runge-Kutta (RK)-HO-FDTD, is proposed. The RK-HO-FDTD method employs the strong stability preserving RK algorithm to substitute time derivates and the Taylor series to replace spatial derivates. The characteristics of the stability, dispersion and convergence are studied. The proposed new method presents a better numerical dispersion and a faster convergence rate both in time and space domain. Compared with the HO-FDTD method, if the mesh size is fixed, it is found that the computational memory of the RK-HO-FDTD method is more than two times of the HO-FDTD method for the same mesh size; but if keeping the same accuracy, the computational cost of the RK-HO-FDTD is the controllable times that of the HO-FDTD method. And compared with the HO-FDTD and RK-MRTD methods, the new scheme presents more accuracy and great potential in electromagnetic problems.