Numerical Simulation of the Stiff System of Equations Within the Spintronic Model.

We consider a stiff system of ordinary differential equations within a spintronic model of the superconductor-ferromagnetic/superconductor Josephson junction (SFS JJ). For some values of parameters, the explicit algorithms failed for numerical solution of this system and special numerical approaches like the implicit two-stage Gauss-Legendre method are required. In our study, we use both explicit and implicit numerical schemes which have been implemented in the respective interactive software on the basis of Wolfram Mathematica technique. In this software, we employ the 4-step explicit Runge-Kutta algorithm and the two-stage Gauss-Legendre method of the 4th accuracy order (also known as the implicit Runge-Kutta scheme), combined with the fixed point method. We analyze the effectiveness of two numerical approaches and demonstrate an advantage of implicit method over the explicit scheme. Results of numerical simulation of superconducting processes in the SFS JJ depending on parameters are presented.