An efficient six-step method for the solution of the Schrodinger equation / Berg Dmitriy B.,Simos T. E. // JOURNAL OF MATHEMATICAL CHEMISTRY. - 2017. - V. 55, l. 8. - P. 1521-1547.

ISSN/EISSN:

0259-9791 / 1572-8897

Type:

Article

Abstract:

In this paper we develop an efficient six-step method for the solution of the Schrodinger 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). 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 Schrodinger 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.

Author keywords:

Schrodinger equation; Multistep methods; Multistage methods; Interval of periodicity; Phase-lag; Phase-fitted; Derivatives of the phase-lag VANISHED PHASE-LAG; INITIAL-VALUE-PROBLEMS; TRIGONOMETRICALLY-FITTED FORMULAS; RUNGE-KUTTA METHODS; PREDICTOR-CORRECTOR METHOD; EXPLICIT 4-STEP METHOD; 8TH ALGEBRAIC ORDER; SYMMETRIC MULTISTEP METHODS; LONG-TIME INTEGRATION; P-STABLE METHOD

DOI:

10.1007/s10910-017-0742-z

Web of Science ID:

ISI:000407134400001

Соавторы в МНС:

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Другие поля

Поле	Значение
Month	SEP
Publisher	SPRINGER
Address	233 SPRING ST, NEW YORK, NY 10013 USA
Language	English
EISSN	1572-8897
Keywords-Plus	VANISHED PHASE-LAG; INITIAL-VALUE-PROBLEMS; TRIGONOMETRICALLY-FITTED FORMULAS; RUNGE-KUTTA METHODS; PREDICTOR-CORRECTOR METHOD; EXPLICIT 4-STEP METHOD; 8TH ALGEBRAIC ORDER; SYMMETRIC MULTISTEP METHODS; LONG-TIME INTEGRATION; P-STABLE METHOD
Research-Areas	Chemistry; Mathematics
Web-of-Science-Categories	Chemistry, Multidisciplinary; Mathematics, Interdisciplinary Applications
Author-Email	tsimos.conf@gmail.com
Number-of-Cited-References	149
Usage-Count-Last-180-days	1
Usage-Count-Since-2013	1
Journal-ISO	J. Math. Chem.
Doc-Delivery-Number	FC9AY