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Effektiva lösningsmetoder för Schrödingerekvationen: En jämförelse
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computational Science.
2013 (Swedish)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

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.

Place, publisher, year, edition, pages
2013. , 14 p.
Series
TVE, TVE 13010 maj
Keyword [sv]
Finita differenser, SBP-SAT, Schrödingerekvationen, Leap-Frog, Crank-Nicholson, Runge-Kutta
National Category
Computer and Information Science Computational Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-208878OAI: oai:DiVA.org:uu-208878DiVA: diva2:655075
Educational program
Master Programme in Engineering Physics
Supervisors
Examiners
Available from: 2013-11-11 Created: 2013-10-10 Last updated: 2013-11-11Bibliographically approved

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Citation style
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