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Journal of Mathematical Chemistry

, Volume 57, Issue 1, pp 119–148 | Cite as

A new multistep method with optimized characteristics for initial and/or boundary value problems

  • Guo-Hua Qiu
  • Chenglian Liu
  • T. E. SimosEmail author
Original Paper

Abstract

In this paper we introduce, for the first time in the literature, an optimized multistage symmetric two-step method. This method is considered as optimized due to the following reasons: (1) it is of tenth-algebraic order scheme, (2) it has obliterated the phase-lag and its first, second, third and fourth derivatives, (3) it has improved stability characteristics, (4) it is a P-stable method. For the new proposed multistage symmetric two-step method we present a full theoretical investigation consisted of: (1) local truncation error and comparative error analysis, (2) stability analysis and (3) interval of periodicity analysis. The effectiveness of the new builded multistage symmetric two-step method is evaluated on the solution of systems of coupled differential equations of the Schrödinger type.

Keywords

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

Mathematics Subject Classification

65L05 

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material

10910_2018_940_MOESM1_ESM.pdf (473 kb)
Supplementary material 1 (pdf 473 KB)

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.School of Electronics and Information EngineeringFuqing Branch of Fujian Normal UniversityFuqingPeople’s Republic of China
  2. 2.Department of Computer Science and TechnologyNeusoft Institute of GuangdongFoshanChina
  3. 3.Department of Mathematics, College of SciencesKing Saud UniversityRiyadhSaudi Arabia
  4. 4.Group of Modern Computational MethodsUral Federal UniversityEkaterinburgRussian Federation
  5. 5.Department of Automation EngineeringTEI of Sterea HellasPsachnaGreece
  6. 6.Section of Mathematics, Department of Civil EngineeringDemocritus University of ThraceXanthiGreece
  7. 7.AthensGreece

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