Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)8380Research ArticleSolving the Hysteresis Loop Calculation Problem for Josephson Junction StacksSerdyukovaS ILaboratory of Information Technologiessis@jinr.ruJoint Institute for Nuclear Research15022014229530008092016Copyright © 2014,2014A 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. The goal of this work is to accelerate the computation of IVC based on numerical solution of the system. A numerical-analytical method was proposed in. 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 g = 1. All calculations were performed using the REDUCE 3.8 system.система джозефсоновских переходоввычисление вольт-амперных характеристикпетля гистерезисазадача Коши для систем нелинейных дифференциальных уравненийметод Рунге-Кутта четвёртого порядка точностиасимптотические формулы решения задачи Коши при больших tчисленно-аналитический метод вычисления ВАХвывод асимптотических формулиспользуя систему REDUCE 3.8[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.][Shukrinov Y.M., Mahfousi F., Pedersen N.F. Investigation of the Breakpoint Region in Stacks with a Finite Number of Intrinsic Josephson Junctions // Phys. Rev. B. - 2007. - Vol. 75. - P. 104508.][Бахвалов Н.С., Жидков Н. П., М. К. Г. Численные методы. - М.: Мир, 1977.][Serdyukova S.I. Numerical-Analytical Method for Computing the Current-Voltage Characteristics for a Stack of Josephson Junctions // Computational Mathematics and Mathematical Physics. - 2012. - Vol. 52, No 11. - Pp. 1590-1596.][Serdyukova S.I. Determination of IVC Breakpoint for Josephson Junction Stack. Periodic and Non-Periodic with g = 0 Boundary Conditions // Particles and Nuclei, Letters. - 2013. - No 3. - Pp. 269-272.][Neun W. REDUCE User’s Guide for Unix Systems. Version 3.8. - Berlin: ZIB, 2004. 6.]