An Iterative High-Accuracy ADI Method for the 3D Parabolic Equation

Abstract

The alternating direction implicit parabolic equation (ADI-PE) method and the Crank–Nicolson parabolic equation (CN-PE) method have been widely used for solving the 3D parabolic equation (3D-PE) in radio wave propagation. The ADI-PE method is more computationally efficient than the CN-PE method. The accuracy of the ADI-PE method is improved by the higher-order Mitchell–Fairweather (MF)-ADI method. This paper presents an iterative high-accuracy (IHA)-ADI method for the 3D parabolic equation. A derivation of the proposed method is presented. The convergence and stability of the proposed method are estimated. Several numerical examples are considered to illustrate the advantages of the proposed method. The results of error analysis and a comparative study show that the proposed method is unconditionally stable and computationally efficient. The proposed method is more numerically accurate than the MF-ADI method.