Numerical-analytical method for computing the current-voltage characteristics for a stack of Josephson junctions

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 wit...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2012-11, Vol.52 (11), p.1590-1596
Main Author: Serdyukova, S. I.
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Boundary conditions
Cauchy problems
Computation
Computational mathematics
Computational Mathematics and Numerical Analysis
Differential equations
Dynamic tests
Electric currents
Josephson junctions
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Neighborhoods
Nonlinear dynamics
Physics
Stacks
Studies
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Summary: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.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542512110115