Advances in Difference Equations (Nov 2021)

Fourth derivative singularly P-stable method for the numerical solution of the Schrödinger equation

  • Ali Shokri,
  • Higinio Ramos,
  • Mohammad Mehdizadeh Khalsaraei,
  • Fikret A. Aliev,
  • Martin Bohner

DOI
https://doi.org/10.1186/s13662-021-03662-9
Journal volume & issue
Vol. 2021, no. 1
pp. 1 – 16

Abstract

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Abstract In this paper, we construct a method with eight steps that belongs to the family of Obrechkoff methods. Due to the explicit nature of the new method, not only does it not require another method as predictor, but it can also be considered as a suitable predictive technique to be used with implicit methods. Periodicity and error terms are studied when applied to solve the radial Schrödinger equation, considering different energy levels. We show its advantages in terms of accuracy, consistency, and convergence in comparison with other methods of the same order appearing in the literature.

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