Structure-preserving exponential time differencing methods for modeling Josephson Junctions

Abstract

Explicit, conformal symplectic, exponential time differencing (ETD) methods have numerous advantages over other well-known and commonly used methods, including structure-preservation, high stability, ease of implementation, and computational efficiency. Such methods are constructed with second and fourth order accuracy through composition techniques using a simple first order scheme. For modeling Josephson Junctions, these ETD schemes regularly exhibit the best balance of efficiency and accuracy when compared to other commonly used methods.