Comparing the Finite -Difference Schemes in the Simulation of Shunted Josephson Junctions

The paper provides investigation of the numerical effects in finite-difference models of RLC-shunted circuit simulating Josephson junction. We study digital models of the circuit obtained by explicit, implicit and semi-explicit Euler methods. The Dormand-Prince 8 ODE solver is used for verification as a reference method. Two aspects of the RLC-shunted Josephson junction model are considered: the dynamical maps (two-dimensional bifurcation diagrams) and chaotic transients existing in the system within a certain parameter range. We show that both explicit and implicit Euler methods distort the dynamical properties, including stretching or compressing the dynamical maps and changing chaotic transient lifetime decay curve. Experiments demonstrate high reliability of the first-order Euler-Cromer method in simulation of the shunted Josephson junction model which yields data close to the reference data. Obtained results bring new accurate chaotic transient lifetime decay equation for the RLC-shunted Josephson junction model.