Geodesic
Numerical-analytical method for computing the current-voltage characteristics for a stack of Josephson junctions
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 11, pp. 2093-2100

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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. 
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     author = {S. I. Serdyukova},
     title = {Numerical-analytical method for computing the current-voltage characteristics for a stack of {Josephson} junctions},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2093--2100},
     publisher = {mathdoc},
     volume = {52},
     number = {11},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_11_a14/}
}
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S. I. Serdyukova. Numerical-analytical method for computing the current-voltage characteristics for a stack of Josephson junctions. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 11, pp. 2093-2100. http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_11_a14/