UDC 519.6 Solving the Hysteresis Loop Calculation Problem for Josephson Junction Stacks S. I. Serdyukova Laboratory of Information Technologies Joint Institute for Nuclear Research 6, Joliot-Curie str., Dubna, Moscow region, Russia, 141980 A detailed investigation of the IVC breakpoint and the breakpoint region width gives important information concerning the peculiarities of stacks with a finite number of intrinsic Josephson junctions. <...> The current-voltage characteristics for a stack of n Josephson junctions is defined from solving the system of n nonlinear differential equations. <...> The current voltage characteristic has the shape of a hysteresis loop. <...> On the back branch of the Hysteresis loop, near the breakpoint Ib, voltage V (I) decreases to zero rapidly. <...> This method showed perfect results in IVC calculations for a stack of 9 and 19 intrinsic Josephson junctions and the computation time reduced by five times approximately. <...> The question of choosing a change-over point from “analytical” to numerical calculation was open. <...> In testing computations the change-over point was taken equal to 2Ib. <...> In the case of periodic boundary conditions an equation, determining the approximate location of Ib, was obtained. <...> This moment we succeeded to develop an algorithm determining the approximate value Ib in more complicated technically case of non-periodic boundary conditions with γ = 1. <...> Key words and phrases: stack of Josephson junctions, computation of current-voltage characteristics, hysteresis loop, Cauchy problem for a system of nonlinear differential equations, fourth-order Runge-Kutta method, long-time asymptotic formulas, a numerical-analytical method, computation of formulas using the REDUCE 3.8 system. 1. <...> For each next I : I = Ik+1, found already ϕl(Ik,Tmax), ˙ϕl(Ik,Tmax) are used as initial data. <...> The dynamics of phase differences ϕl(t) had been simulated by solving the equation system (2) using the fourth order Runge-Kutta method [2]. <...> After simulation of the phase differences dynamics the voltages on each junction were calculated as ∂ϕl/∂t = The average of the voltage ¯ Vl is given by ¯ Vl = ∑ l′=1 n Al,l′ Vl′ . 1 Tmax −Tmin ∑ l=1 n Tmax ∫ Tmin Finally the total voltage V of the stack is obtained by summing these averages: V = Vl. <...> The fundamental matrices D (whose <...>