Efficient Integration of High-Order Stencils Into the ADI-FDTD Method

Incorporating standard high-order spatial approximations in the alternating-direction implicit (ADI) finite-difference time-domain method does not suffice for improving the technique's accuracy, as these operators are capable of reducing spatial errors only. We herein develop an alternative design procedure, which results in the construction of finite-difference expressions that ameliorate the combined space-time flaws. In essence, it is shown that three error formulas are derived from the individual implicit equations, provided that the ADI updates are treated as a single-step process. Then, more efficient spatial expressions can be extracted through proper manipulation of these formulas and subsequent application of error-controlling concepts.