Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/6966
Title: Classical time splitting approaches and their error anlyses for nonlinear differential equations
Other Titles: Lineer olmayan diferansiyel denklemler için klasik ayırma yaklaşımları ve hata analizleri
Authors: Tanoğlu, Gamze
Hacısalihoğlu, Elif
Keywords: Differential equations
Operator splitting methods
Nonlinear differential equation
Lie - Trotter splitting
Strang - Marchuk splitting
Symmetrically weighted sequential
Issue Date: Jun-2018
Publisher: Izmir Institute of Technology
Source: Hacısalihoğlu, E. (2018). Classical time splitting approaches and their error anlyses for nonlinear differential equations. Unpublished master's thesis, Izmir Institute of Technology, Izmir, Turkey
Abstract: In this thesis, Lie - Trotter splitting, Strang - Marchuk splitting and symmetrically weighted sequential (SWS) splitting methods which are known as classical operator splitting methods are considered to find the numerical solution of the various ordinary differential equations (ODEs) and partial differential equations (PDEs). We also presented their error analyses in order to show advantages and disadvantages of these methods. Firstly, we considered simple linear and nonlinear ODE examples to motivate for the classical operator splitting methods. Then, two numerical examples which consist of a kinetic model of phage infection and the Newell - Whitehead - Segel (NWS) equation are studied. All these examples show that the operator splitting methods are a powerful technique with respect to the accuracy and robustness.
Bu tezde klasik operatör ayırma metodları olarak bilinen Lie - Trotter ayırma, Strang - Marchuk ayırma ve symmetrically weighted sequential (SWS) ayırma metodları çeşitli adi diferansiyel denklemlerin ve kısmi diferansiyel denklemlerin sayısal çözümünü bulmak için ele alınmıştır. Ayrıca bu yöntemlerin avantajlarını ve dezavantajlarını göstermek için hata analizlerini sunduk. İlk olarak, klasik operatör ayırma metodlarına motive olmak için basit lineer ve lineer olmayan ODE örneklerini düşündük. Daha sonra, bir faj enfeksiyonun kinetic bir modelinden ve Newell - Whitehead - Segel (NWS) denkleminden oluşan iki sayısal örnek üzerinde çalışılmıştır. Bütün bu örnekler operatör ayırma metodlarının doğruluk ve sağlamlık açısından güçlü bir teknik olduğunu göstermektedir.
Description: Thesis (Master)--Izmir Institute of Technology, Mathematics, Izmir, 2018
Includes bibliographical references (leaves: 60-62)
Text in English; Abstract: Turkish and English
URI: http://hdl.handle.net/11147/6966
Appears in Collections:Master Degree / Yüksek Lisans Tezleri

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