Exponential Methods for the Time Integration of Schroedinger Equation

Journal Article · Thu Sep 30 00:00:00 EDT 2010 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.3498247· OSTI ID:21428579

Cano, B; Gonzalez-Pachon, A ^[1]

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1. Faculty of Sciences, C/Doctor Mergelina, s/n, 47011-Valladolid (Spain)

We consider exponential methods of second order in time in order to integrate the cubic nonlinear Schroedinger equation. We are interested in taking profit of the special structure of this equation. Therefore, we look at symmetry, symplecticity and approximation of invariants of the proposed methods. That will allow to integrate till long times with reasonable accuracy. Computational efficiency is also our aim. Therefore, we make numerical computations in order to compare the methods considered and so as to conclude that explicit Lawson schemes projected on the norm of the solution are an efficient tool to integrate this equation.

• OSTI ID: 21428579
• Journal Information: AIP Conference Proceedings, Vol. 1281, Issue 1; Conference: ICNAAM 2010: International conference of numerical analysis and applied mathematics 2010, Rhodes (Greece), 19-25 Sep 2009; Other Information: DOI: 10.1063/1.3498247; (c) 2010 American Institute of Physics; ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ACCURACY
APPROXIMATIONS
COMPARATIVE EVALUATIONS
INTEGRAL EQUATIONS
NONLINEAR PROBLEMS
RUNGE-KUTTA METHOD
SCHROEDINGER EQUATION
SYMMETRY
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
EQUATIONS
EVALUATION
ITERATIVE METHODS
MATHEMATICAL SOLUTIONS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
WAVE EQUATIONS