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Journal of Mathematical Chemistry

, Volume 57, Issue 1, pp 232–262 | Cite as

New multiple stages scheme with improved properties for second order problems

  • V. N. Kovalnogov
  • R. V. Fedorov
  • D. V. Suranov
  • T. E. Simos
Original Paper
  • 30 Downloads

Abstract

A new multiple stages two–step scheme with best possible properties on phase and stability is introduced, for the first time in the literature. For this scheme we present a full theoretical, numerical and computational analysis. The ability of the new multiple stages scheme is examined by applying it on the solution of systems of coupled differential equations.

Keywords

Phase-lag Derivative of the phase-lag Initial value problems Oscillating solution Symmetric Hybrid Multistep Schrödinger equation 

Mathematical Subject Classification

65L05 

Notes

Acknowledgements

The reported research was funded by Russian Foundation for Basic Research and the government of the Ulyanovsk region of the Russian Federation, Grant No. \(\text {18-48-730013}\).

Compliance with ethical standards

Conflicts of interest

The authors declare that they have no conflict of interest.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • V. N. Kovalnogov
    • 1
  • R. V. Fedorov
    • 1
  • D. V. Suranov
    • 1
  • T. E. Simos
    • 2
    • 3
    • 4
    • 5
    • 6
  1. 1.Group of Numerical and Applied Mathematics on Urgent Problems of Energy and Power Engineering, Faculty of Power EngineeringUlyanovsk State Technical UniversityUlyanovskRussian Federation
  2. 2.Department of Mathematics, College of SciencesKing Saud UniversityRiyadhSaudi Arabia
  3. 3.Group of Modern Computational MethodsUral Federal UniversityEkaterinburgRussian Federation
  4. 4.Department of Automation EngineeringTEI of Sterea Hellas, GRPsachnaGreece
  5. 5.Section of Mathematics, Department of Civil EngineeringDemocritus University of ThraceXanthiGreece
  6. 6.AthensGreece

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