New approaches for solving nonlinear oscillation problems
Korkut Uysal, Sıla Övgü, author.

New approaches for solving nonlinear oscillation problems

Korkut Uysal, Sıla Övgü, author.

Yazar Ek Girişi
Korkut Uysal, Sıla Övgü, author.

Fiziksel Tanımlama
x, 115 leaves:+ 1 computer laser optical disc.

This thesis proposes two different numerical methods for solving nonlinear oscillation problems which appear in engineering and physics. Thus, the study is conducted in two parts. The first part introduces and analyzes the new iterative splitting method. In the construction of this method I utilize both the iterative splitting process and nonlinear Magnus expansion. Due to the fact that the iterative splitting procedure is employed, the constructed method can also be considered as a kind of operator splitting method. The second part presents a new linearization technique, based on the Newton-Raphson method and the Fréchet derivatives, for oscillation systems. Duffing oscillator and damped oscillator are used for testing the methods, respectively. Moreover, the proposed iterative splitting method and the proposed linearization technique are applied to both Van-der Pol equation and cubic nonlinear Schrödinger equation. Although the examples considered are a small sample of nonlinear oscillation equations, it is believed that the methods are easily adapted to solve such problems numerically.

Konu Başlığı
Nonlinear oscillations.

Yazar Ek Girişi
Tanoğlu, Gamze

Tüzel Kişi Ek Girişi
İzmir Institute of Technology. Mathematics.

Tek Biçim Eser Adı
Thesis (Doctoral)--İzmir Institute of Technology: Mathematics.
İzmir Institute of Technology: Mathematics--Thesis (Doctoral).

Elektronik Erişim
Access to Electronic Versiyon.

LibraryMateryal TürüDemirbaş NumarasıYer NumarasıDurumu/İade Tarihi
IYTE LibraryTezT001357QA867.5 .K84 2015Tez Koleksiyonu