Abstract:
A numerical-analytical method was proposed for analyzing dynamic processes in stacks of Josephson junctions. The Cauchy problem for a system of $n$ nonlinear differential equations was solved. Formal “approximate solutions” at long times were constructed. The results based on these solutions agree with numerical results up to a small neighborhood of a critical point where the voltage drops rapidly to zero. The numerical-analytical method was tested by computing the hysteresis loop for stacks of 9 and 19 Josephson junctions of various structures. Good agreement was found with numerical results. Moreover, the computation time was reduced by more than five times.
Key words: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, computation of formulas with the use of the REDUCE 3.8 system.
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