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Numerical Simulation of the Stiff System of Equations Within the Spintronic Model

  • Pavlina Kh. Atanasova
  • Stefani A. PanayotovaEmail author
  • Elena V. Zemlyanaya
  • Yury M. Shukrinov
  • Ilhom R. Rahmonov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11189)

Abstract

We consider a stiff system of ordinary differential equations within a spintronic model of the superconductor-ferromagnetic/superconductor Josephson junction (SFS JJ). For some values of parameters, the explicit algorithms failed for numerical solution of this system and special numerical approaches like the implicit two-stage Gauss-Legendre method are required. In our study, we use both explicit and implicit numerical schemes which have been implemented in the respective interactive software on the basis of Wolfram Mathematica technique. In this software, we employ the 4-step explicit Runge-Kutta algorithm and the two-stage Gauss–Legendre method of the 4th accuracy order (also known as the implicit Runge-Kutta scheme), combined with the fixed point method. We analyze the effectiveness of two numerical approaches and demonstrate an advantage of implicit method over the explicit scheme. Results of numerical simulation of superconducting processes in the SFS JJ depending on parameters are presented.

Keywords

Stiff system Implicit method Spintronic model 

Notes

Acknowledgement

The work is supported by project FP17-FMI-008, Bulgaria, by the JINR–Bulgaria cooperation program, by the grant of AYSS of JINR with the project 18-302-08 and by the Russian Foundation for Basic Research (projects 18-52-45011\(\_\)Ind, 17-01-00661, 18-02-00318).

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Pavlina Kh. Atanasova
    • 1
  • Stefani A. Panayotova
    • 1
    Email author
  • Elena V. Zemlyanaya
    • 2
    • 3
  • Yury M. Shukrinov
    • 2
    • 3
  • Ilhom R. Rahmonov
    • 2
    • 4
  1. 1.University of Plovdiv Paisii HilendarskiPlovdivBulgaria
  2. 2.Joint Institute of Nuclear ResearchDubnaRussia
  3. 3.Dubna State UniversityDubnaRussia
  4. 4.Umarov Physical Technical Institute, TASDushanbeTajikistan

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