Effektiva lösningsmetoder för Schrödingerekvationen : En jämförelse

Effektiva lösningsmetoder för Schrödingerekvationen : En jämförelse

In this paper the rate of convergence, speed of execution and symplectic properties of the time-integrators Leap-Frog (LF2), fourth order Runge-Kutta(RK4) and Crank-Nicholson (CN2) have been studied. This was done by solving the one-dimensional model for a particle in a box (Dirichlet-conditions). T...

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Bibliographic Details
Main Author: Christoffer, Zakrisson
Format: Others
Language:Swedish
Published: Uppsala universitet, Tillämpad beräkningsvetenskap 2013
Subjects:
Finita differenser
SBP-SAT
Schrödingerekvationen
Leap-Frog
Crank-Nicholson
Runge-Kutta
Computer and Information Sciences
Data- och informationsvetenskap
Computational Mathematics
Beräkningsmatematik
Online Access:http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-208878
Description
Summary:In this paper the rate of convergence, speed of execution and symplectic properties of the time-integrators Leap-Frog (LF2), fourth order Runge-Kutta(RK4) and Crank-Nicholson (CN2) have been studied. This was done by solving the one-dimensional model for a particle in a box (Dirichlet-conditions). The results show that RK4 is the fastest in achieving higher tolerances, while CN2 is the fastest in achieving lower tolerances. Fourth order corrections of LF (LF4)and CN (CN4) were also studied, though these showed no improvements overLF2 and CN2. All methods were shown to exhibit symplectic behavior.

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