# An efficient and computational effective method for second order problems

An efficient and computational effective method for second order problems An efficient and computational effective algorithm is introduced, for the first time in the literature, in the present paper. The main properties of the scheme are: (1) the algorithm is a two-step scheme, (2) the algorithm is symmetric one, (3) it is a hight algebraic order scheme (i.e of eight algebraic order), (4) it is a three-stages algorithm, (5) the first layer of the new method is based on an approximation to the point $$x_{n-1}$$ x n - 1 , (6) the scheme has vanished phase-lag and its first, second and third derivatives, (7) the new proposed algorithm has an interval of periodicity equal to $$\left( 0, 9.8 \right)$$ 0 , 9.8 . For the present new scheme we study: (1) its construction, (2) its error analysis (3) its stability analysis. Finally, the investigation of the effectiveness of the new algorithm leads to its application to systems of differential equations arising from the Schrödinger equation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Mathematical Chemistry Springer Journals

# An efficient and computational effective method for second order problems

, Volume 55 (8) – May 16, 2017
20 pages

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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/s10910-017-0753-9
Publisher site
See Article on Publisher Site

### Abstract

An efficient and computational effective algorithm is introduced, for the first time in the literature, in the present paper. The main properties of the scheme are: (1) the algorithm is a two-step scheme, (2) the algorithm is symmetric one, (3) it is a hight algebraic order scheme (i.e of eight algebraic order), (4) it is a three-stages algorithm, (5) the first layer of the new method is based on an approximation to the point $$x_{n-1}$$ x n - 1 , (6) the scheme has vanished phase-lag and its first, second and third derivatives, (7) the new proposed algorithm has an interval of periodicity equal to $$\left( 0, 9.8 \right)$$ 0 , 9.8 . For the present new scheme we study: (1) its construction, (2) its error analysis (3) its stability analysis. Finally, the investigation of the effectiveness of the new algorithm leads to its application to systems of differential equations arising from the Schrödinger equation.

### Journal

Journal of Mathematical ChemistrySpringer Journals

Published: May 16, 2017

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