New approaches for solving nonlinear oscillation problems

tarafından

Korkut Uysal, Sıla Övgü, author.

Başlık

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New approaches for solving nonlinear oscillation problems

Yazar

:
Korkut Uysal, Sıla Övgü, author.

Yazar Ek Girişi

:
Korkut Uysal, Sıla Övgü, author.

Fiziksel Tanımlama

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

Özet

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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

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Nonlinear oscillations.

Yazar Ek Girişi

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Tanoğlu, Gamze

Tüzel Kişi Ek Girişi

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İzmir Institute of Technology. Mathematics.

Tek Biçim Eser Adı

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Thesis (Doctoral)--İzmir Institute of Technology: Mathematics.

İzmir Institute of Technology: Mathematics--Thesis (Doctoral).

Elektronik Erişim

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Library | Materyal Türü | Demirbaş Numarası | Yer Numarası | Durumu/İade Tarihi |
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IYTE Library | Tez | T001357 | QA867.5 .K84 2015 | Tez Koleksiyonu |