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Title: Higher order symplectic methods for separable Hamiltonian equations master of science
Authors: Tanoğlu, Gamze
Gündüz, Hakan
Issue Date: 2010
Publisher: Izmir Institute of Technology
Abstract: The higher order, geometric structure preserving numerical integrators based on the modified vector fields are used to construct discretizations of separable Hamiltonian systems. This new approach is called as modifying integrators. Modified vector fields can be used to construct high-order structure-preserving numerical integrators for both ordinary and partial differential equations. In this thesis, the modifying vector field idea is applied to Lobatto IIIA-IIIB methods for linear and nonlinear ODE problems. In addition, modified symplectic Euler method is applied to separable Hamiltonian PDEs. Stability and consistency analysis are also studied for these new higher order numerical methods. Von Neumann stability analysis is studied for linear and nonlinear PDEs by using modified symplectic Euler method. The proposed new numerical schemes were applied to the separable Hamiltonian systems.
Description: Thesis (Master)--Izmir Institute of Technology, Mathematics, Izmir, 2010
Includes bibliographical references (leaves: 82-83)
Text in English; Abstract: Turkish and English
x, 94 leaves
Appears in Collections:Master Degree / Yüksek Lisans Tezleri

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