ABSTRACTA compact fourth‐order six‐stages split‐step finite‐difference time‐domain method is developed, which is based on the compact fourth‐order scheme. The proposed method improves the efficiency of computation by reducing the bandwidth of the matrix to be inversed from seven to five for the fourth‐order scheme. Furthermore, the proposed method is proven to be unconditionally stable. The numerical dispersion error of this new approach is studied by comparison to the original second‐order method and fourth‐order method. © 2014 Wiley Periodicals, Inc. Microwave Opt Technol Lett 56:1031–1036, 2014