New three-stages symmetric six-step finite difference method with vanished phase-lag and its derivatives up to sixth derivative for second order initial and/or boundary value problems with periodical and/or oscillating solutions

In this paper, for the first time in the literature, we develop a symmetric three-stages six-step method with the following characteristics; the method is a symmetric hybrid (multistages) six-step method, is of three-stages, is of twelfth algebraic order, has vanished the phase-lag and has vanished...

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Vydané v:	Journal of mathematical chemistry Ročník 56; číslo 8; s. 2267 - 2301
Hlavní autori:	Alolyan, Ibraheem, Simos, T. E.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Cham Springer International Publishing 01.09.2018 Springer Nature B.V
Predmet:	Boundary value problems Chemistry Chemistry and Materials Science Computing time Derivatives Error analysis Finite difference method Math. Applications in Chemistry Original Paper Periodic variations Phase lag Physical Chemistry Schrodinger equation Stability analysis Theoretical and Computational Chemistry Interval of periodicity Multistep methods Derivatives of the phase-lag Phase-lag Phase-fitted Schrödinger equation Multistage methods
ISSN:	0259-9791, 1572-8897
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Popis
Shrnutí:	In this paper, for the first time in the literature, we develop a symmetric three-stages six-step method with the following characteristics; the method is a symmetric hybrid (multistages) six-step method, is of three-stages, is of twelfth algebraic order, has vanished the phase-lag and has vanished the derivatives of the phase-lag up to order six. A detailed theoretical, numerical and computational analysis is also presented. The above analyses consist of: the construction of the new six-step pair, the presentation of the computed local truncation error of the new six-step pair, the comparative error analysis of the new six-step pair with other six-step pairs of the same family which are: the classical six-step pair of the family (i.e. the six-step pair with constant coefficients), the recently proposed six-step pair of the same family with vanished phase-lag and its first derivative, the recently proposed six-step pair of the same family with vanished phase-lag and its first and second derivatives, the recently proposed six-step pair of the same family with vanished phase-lag and its first, second and third derivatives, the recently proposed six-step pair of the same family with vanished phase-lag and its first, second, third and fourth derivatives and finally, the recently proposed six-step pair of the same family with vanished phase-lag and its first, second, third, fourth and fifth derivatives the stability and the interval of periodicity analysis for the new obtained six-step pair and finally the investigation of the accuracy and computational efficiency of the new developed six-step pair for the solution of the Schrödinger equation. The theoretical, numerical and computational achievements lead to the conclusion that the new produced three-stages symmetric six-step pair is more efficient than other known or recently developed finite difference pairs of the literature.
Bibliografia:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	0259-9791 1572-8897
DOI:	10.1007/s10910-018-0888-3