An efficient six-step method for the solution of the Schrödinger equation

An efficient six-step method for the solution of the Schrödinger equation In this paper we develop an efficient six-step method for the solution of the Schrödinger equation and related problems. The characteristics of the new obtained scheme are: It is of twelfth algebraic order. It has three stages. It has vanished phase-lag. It has vanished its derivatives up to order two. All the stages of the scheme are approximations on the point $$x_{n+3}$$ x n + 3 . 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 phase-lag 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Mathematical Chemistry Springer Journals

An efficient six-step method for the solution of the Schrödinger equation

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Publisher
Springer International Publishing
Copyright
Copyright © 2017 by Springer International Publishing Switzerland
Subject
Chemistry; Physical Chemistry; Theoretical and Computational Chemistry; Math. Applications in Chemistry
ISSN
0259-9791
eISSN
1572-8897
D.O.I.
10.1007/s10910-017-0742-z
Publisher site
See Article on Publisher Site

Abstract

In this paper we develop an efficient six-step method for the solution of the Schrödinger equation and related problems. The characteristics of the new obtained scheme are: It is of twelfth algebraic order. It has three stages. It has vanished phase-lag. It has vanished its derivatives up to order two. All the stages of the scheme are approximations on the point $$x_{n+3}$$ x n + 3 . 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 phase-lag 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.

Journal

Journal of Mathematical ChemistrySpringer Journals

Published: Mar 22, 2017

References

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