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Numerical Algorithms

, Volume 80, Issue 2, pp 557–593 | Cite as

A new family of three-stage two-step P-stable multiderivative methods with vanished phase-lag and some of its derivatives for the numerical solution of radial Schrödinger equation and IVPs with oscillating solutions

  • Ali ShokriEmail author
  • Mohammad Mehdizadeh Khalsaraei
  • Mortaza Tahmourasi
  • Raquel Garcia-Rubio
Original Paper
  • 27 Downloads

Abstract

A new family of three-stage two-step methods are presented in this paper. These methods are of algebraic order 12 and have an important P-stability property. To make these methods, vanishing phase-lag and some of its derivatives have been used. The main structure of these methods are multiderivative, and the combined phases have been applied for expanding stability interval and for achieving P-stability. The advantage of the new methods in comparison with similar methods, in terms of efficiency, accuracy, and stability, has been showed by the implementation of them in some important problems, including the radial time-independent Schrödinger equation during the resonance problems with the use of the Woods-Saxon potential, undamped Duffing equation, etc.

Keywords

Phase-fitting Schrödinger equation Phase-lag Ordinary differential equations P-stable Multiderivative methods 

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Notes

Acknowledgments

The authors wish to thank the Professor T. Mitsui for his careful reading the original draft of this article patiently and providing valuable feedback in order to correct it. The authors also express their gratitude to the anonymous referees who read the paper accurately and presented elaborate recommendations.

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Authors and Affiliations

  1. 1.Faculty of Mathematical ScienceUniversity of MaraghehMaraghehIran
  2. 2.IME Univeristy SalamancaSalamancaSpain

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