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Title: A Family of Symmetric Linear Multistep Methods for the Numerical Solution of the Schroedinger Equation and Related Problems

Abstract

We develop a new family of explicit symmetric linear multistep methods for the efficient numerical solution of the Schroedinger equation and related problems with oscillatory solution. The new methods are trigonometrically fitted and have improved intervals of periodicity as compared to the corresponding classical method with constant coefficients and other methods from the literature. We also apply the methods along with other known methods to real periodic problems, in order to measure their efficiency.

Authors:
 [1];  [2]
  1. Department of Finance and Auditing, School of Management and Economics, Technological Educational Institute of Kalamata, GR-241 00 Antikalamos (Greece)
  2. Laboratory of Computational Sciences, Department of Computer Science and Technology, Faculty of Sciences and Technology, University of Peloponnese, GR-22 100 Tripolis (Greece)
Publication Date:
OSTI Identifier:
21428581
Resource Type:
Journal Article
Journal Name:
AIP Conference Proceedings
Additional Journal Information:
Journal Volume: 1281; Journal Issue: 1; Conference: ICNAAM 2010: International conference of numerical analysis and applied mathematics 2010, Rhodes (Greece), 19-25 Sep 2009; Other Information: DOI: 10.1063/1.3498259; (c) 2010 American Institute of Physics; Journal ID: ISSN 0094-243X
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EFFICIENCY; FUNCTIONAL ANALYSIS; INTEGRAL EQUATIONS; NUMERICAL SOLUTION; PERIODICITY; SCHROEDINGER EQUATION; SYMMETRY; DIFFERENTIAL EQUATIONS; EQUATIONS; MATHEMATICAL SOLUTIONS; MATHEMATICS; PARTIAL DIFFERENTIAL EQUATIONS; VARIATIONS; WAVE EQUATIONS

Citation Formats

Anastassi, Z A, and Simos, T E. A Family of Symmetric Linear Multistep Methods for the Numerical Solution of the Schroedinger Equation and Related Problems. United States: N. p., 2010. Web. doi:10.1063/1.3498259.
Anastassi, Z A, & Simos, T E. A Family of Symmetric Linear Multistep Methods for the Numerical Solution of the Schroedinger Equation and Related Problems. United States. https://doi.org/10.1063/1.3498259
Anastassi, Z A, and Simos, T E. 2010. "A Family of Symmetric Linear Multistep Methods for the Numerical Solution of the Schroedinger Equation and Related Problems". United States. https://doi.org/10.1063/1.3498259.
@article{osti_21428581,
title = {A Family of Symmetric Linear Multistep Methods for the Numerical Solution of the Schroedinger Equation and Related Problems},
author = {Anastassi, Z A and Simos, T E},
abstractNote = {We develop a new family of explicit symmetric linear multistep methods for the efficient numerical solution of the Schroedinger equation and related problems with oscillatory solution. The new methods are trigonometrically fitted and have improved intervals of periodicity as compared to the corresponding classical method with constant coefficients and other methods from the literature. We also apply the methods along with other known methods to real periodic problems, in order to measure their efficiency.},
doi = {10.1063/1.3498259},
url = {https://www.osti.gov/biblio/21428581}, journal = {AIP Conference Proceedings},
issn = {0094-243X},
number = 1,
volume = 1281,
place = {United States},
year = {Thu Sep 30 00:00:00 EDT 2010},
month = {Thu Sep 30 00:00:00 EDT 2010}
}