In this work, a stable and explicit MOT solver that employs a predictor-corrector scheme to efficiently solve the time domain VEFIE is described. Spatial discretization of VEFIE is carried out in the same way as the implicit MOT-VFIE solver but the time marching is constructed in the form of a traditional PE(CE)m scheme. The stability and accuracy of the time marching are controlled using successive over relaxation (SOR) applied at each repetition of the corrector step. As opposed to its implicit counterpart, the explicit solver requires at every time step inversion of a matrix system with a Gram matrix that is sparse and well-conditioned regardless of time step size. It should be noted here that the PE(CE)m scheme can be constructed using classical polynomial based methods (e.g., Adam-Moulton, Adam-Bashforth, backward difference formula) or novel numerical methods based on exponential fitting (A. Glaser and V. Rokhlin, J. Sci. Comput., 38(3), 368-399, 2009). Unlike the classical explicit MOT solvers, the proposed solver can work with large time steps as in its implicit counterpart. Numerical results demonstrate that it provides faster solution especially for small permittivity values compared to implicit MOT solver, and is capable of providing stable solution even when the implicit solver fails.
