A High Accuracy Modified FDTD(2,4) Scheme with More Relaxed Stability Condition

A relaxed modified FDTD (2,4) scheme (RM24) is proposed to alleviate the Courant condition. Extending the Modified FDTD (2,4) (M24) scheme, we incorporate third-degree spatial difference terms with fourth-order accuracy into the time-stepping formulas to relax the constraints of the Courant condition. Through the optimization of both the coefficients of the third-degree terms and the original coefficients in the M24 scheme, the global numerical dispersion error of the RM24 scheme is reduced to the minimum. For wideband applications, by selecting the above coefficients corresponding to an appropriate grid resolution while maintaining the spatial step size constant, the numerical dispersion error of the RM24 scheme can be further reduced within the operational frequency band. Numerical results demonstrate that the proposed RM24 scheme with large Courant numbers effectively ensures the numerical stability and low numerical dispersion characteristics, thereby enhancing its capability to efficiently achieve accurate results in long-time simulations and electrically large-scale scenarios.