Simulation of Dynamic Processes in Long Josephson Junctions. The Problem on Calculating the Current–Voltage Characteristics. Numerical Method for Estimating the Round-Off Error Growth Rate

As a rule, current–voltage characteristics are numerically calculated using the fourth-order Runge–Kutta scheme. The calculations are carried out over large time intervals and, at each time step, the right-hand sides of the equations are recalculated four times. To reduce the computation time, it is...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2022, Vol.62 (1), p.1-9
Main Authors: Zuev, M. I., Serdyukova, S. I.
Format: Article
Language:English
Subjects:
Algorithms
Computational Mathematics and Numerical Analysis
Current voltage characteristics
General Numerical Methods
Josephson junctions
Mathematical analysis
Mathematics
Mathematics and Statistics
Numerical methods
Roundoff error
Runge-Kutta method
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Summary:As a rule, current–voltage characteristics are numerically calculated using the fourth-order Runge–Kutta scheme. The calculations are carried out over large time intervals and, at each time step, the right-hand sides of the equations are recalculated four times. To reduce the computation time, it is proposed to replace the Runge–Kutta scheme by an “explicit” second-order scheme. For and all , estimations of guaranteeing the boundedness of the round-off error growth rate were proved, where is the operator of the transition from layer to layer and are the grid steps in , respectively. In this work a numerico-analytical algorithm for estimating the round-off errors is developed for all . Their boundedness over the entire interval of calculating the current–voltage characteristics of long Josephson junctions when using the proposed scheme is proved. The calculations were carried out on a “Govorun” supercomputer with the REDUCE system.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542522010122