High order computationally economical six-step method with vanished phase-lag and its derivatives for the numerical solution of the Schrodinger equation / Berg Dmitriy B.,Simos T. E. // JOURNAL OF MATHEMATICAL CHEMISTRY. - 2017. - V. 55, l. 4. - P. 987-1013.

ISSN/EISSN:

0259-9791 / 1572-8897

Type:

Article

Abstract:

A computationally economical symmetric six-step algorithm with high algebraic and phase-lag order is obtained in this paper, for the first time in the literature. Some characteristics of the new algorithm are: (1) algebraic order ten tenth, (2) eliminated phase-lag and its first, second, third, fourth and fifth derivatives, (3) the first layer is an approximation on the point and no at the usual point . A detailed analysis is also presented. In order to evaluate the efficiency of the new algorithm, we compare it with other well known and recently developed algorithms on three stages of evaluation: (1) evaluation based on local truncation error. (2) Evaluation based on stability analysis. (3) Evaluation based on accuracy and computational efficiency of the numerical approximation of the Schrodinger equation. Based on the above analysis, we arrive to the conclusion that the new developed method is more effective than other well known or recently produced methods of the literature.

Author keywords:

Schrodinger equation; Multistep methods; Multistage methods; Interval of periodicity; Phase-lag; Phase-fitted; Derivatives of the phase-lag INITIAL-VALUE-PROBLEMS; TRIGONOMETRICALLY-FITTED FORMULAS; PREDICTOR-CORRECTOR METHOD; EXPLICIT 4-STEP METHOD; KUTTA-NYSTROM METHODS; 8TH ALGEBRAIC ORDER; SYMMETRIC MULTISTEP METHODS; P-STABLE METHOD; ORBITAL PROBLEMS; 4TH DERIVATIVES

DOI:

10.1007/s10910-016-0714-8

Web of Science ID:

ISI:000396054200005

Соавторы в МНС:

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Другие поля

Поле	Значение
Month	APR
Publisher	SPRINGER
Address	233 SPRING ST, NEW YORK, NY 10013 USA
Language	English
EISSN	1572-8897
Keywords-Plus	INITIAL-VALUE-PROBLEMS; TRIGONOMETRICALLY-FITTED FORMULAS; PREDICTOR-CORRECTOR METHOD; EXPLICIT 4-STEP METHOD; KUTTA-NYSTROM METHODS; 8TH ALGEBRAIC ORDER; SYMMETRIC MULTISTEP METHODS; P-STABLE METHOD; ORBITAL PROBLEMS; 4TH DERIVATIVES
Research-Areas	Chemistry; Mathematics
Web-of-Science-Categories	Chemistry, Multidisciplinary; Mathematics, Interdisciplinary Applications
Author-Email	tsimos.conf@gmail.com
ResearcherID-Numbers	Simos, Theodore/H-6033-2011
Number-of-Cited-References	145
Journal-ISO	J. Math. Chem.
Doc-Delivery-Number	EN5OD