Higher order symplectic methods for separable hamiltonian equations master of science
by
Gündüz, Hakan.
Title
:
Higher order symplectic methods for separable hamiltonian equations master of science
Author
:
Gündüz, Hakan.
Personal Author
:
Gündüz, Hakan.
Publication Information
:
[s.l.]: [s.n.], 2010.
Physical Description
:
x, 94 leaves.: ill. + 1 computer laser optical disc.
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.
Subject Term
:
Differential equations.
Hamiltonian systems.
Symplectic geometry.
Added Author
:
Tanoğlu, Gamze.
Added Corporate Author
:
İzmir Institute of Technology. Mathematics.
Added Uniform Title
:
Thesis (Master)--İzmir Institute of Technology: Mathematics.
İzmir Institute of Technology: Mathematics--Thesis (Master).
Electronic Access
:
Library | Material Type | Item Barcode | Shelf Number | Status |
---|
IYTE Library | Thesis | T000826 | QA371 .G97 2010 | Tez Koleksiyonu |
IYTE Library | Supplementary CD-ROM | ROM1599 | QA371 .G97 2010 EK1 | Tez Koleksiyonu |