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Title: Comparison of geometric integrator methods for Hamilton systems
Authors: Tanoğlu, Gamze
İneci, Pınar
Issue Date: 2009
Publisher: Izmir Institute of Technology
Abstract: Geometric numerical integration is relatively new area of numerical analysis The aim of a series numerical methods is to preserve some geometric properties of the flow of a differential equation such as symplecticity or reversibility In this thesis, we illustrate the effectiveness of geometric integration methods. For this purpose symplectic Euler method, adjoint of symplectic Euler method, midpoint rule, Störmer-Verlet method and higher order methods obtained by composition of midpoint or Störmer-Verlet method are considered as geometric integration methods. Whereas explicit Euler, implicit Euler, trapezoidal rule, classic Runge-Kutta methods are chosen as non-geometric integration methods. Both geometric and non-geometric integration methods are applied to the Kepler problem which has three conserved quantities: energy, angular momentum and the Runge-Lenz vector, in order to determine which those quantities are preserved better by these methods.
Description: Thesis (Master)--Izmir Institute of Technology, Mathematics, Izmir, 2009
Includes bibliographical references (leaves: 79)
Text in English; Abstract: Turkish and English
xii, 115leaves
Appears in Collections:Master Degree / Yüksek Lisans Tezleri

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