An efficient sixstep method for the solution of the Schrödinger equation
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Abstract
In this paper we develop an efficient sixstep method for the solution of the Schrödinger equation and related problems. The characteristics of the new obtained scheme are: This method is developed for the first time in the literature. A detailed theoretical analysis of the method is also presented. In the theoretical analysis, a comparison with the the classical scheme of the family (i.e. scheme with constant coefficients) and with recently developed algorithm of the family with eliminated phaselag and its first derivative is also given. Finally, we study the accuracy and computational effectiveness of the new developed algorithm for the on the approximation of the solution of the Schrödinger equation. The above analysis which is described in this paper, leads to the conclusion that the new algorithm is more efficient than other known or recently obtained schemes of the literature.

It is of twelfth algebraic order.

It has three stages.

It has vanished phaselag.

It has vanished its derivatives up to order two.

All the stages of the scheme are approximations on the point \(x_{n+3}\).
Keywords
Schrödinger equation Multistep methods Multistage methods Interval of periodicity Phaselag Phasefitted Derivatives of the phaselagMathematics Subject Classification
65L05Notes
Author contributions
Authors whose names appear on the submission have contributed sufficiently to the scientific work and therefore share collective responsibility and accountability for the results.
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest.
Informed consent
Consent to submit has been received explicitly from all coauthors, as well as from the responsible authorities—tacitly or explicitly—at the institute/organization where the work has been carried out, before the work is submitted.
Supplementary material
10910_2017_742_MOESM1_ESM.pdf (192 kb)
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