Dejenere olan bir boyutlu nonlineer parabolik denklem için sonlu farklar yöntemi
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Date
2017
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Publisher
İstanbul Beykent Üniversitesi
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info:eu-repo/semantics/openAccess
Abstract
Tezde bazı özelliklere sahip olan, örneğin dejenere olabilen nonlineer denklemlerin söz konusu özelliklerini dikkate alarak çözümün tüm fiziksel özelliklerini düzgün ifade edebilen sonlu fark algoritmaları önerilmiştir. Bu amaçla önce bazı denklemlerin gerçek çözümleri bulunmuştur. Bu çözümler sonlu farklar yöntemi ile elde edilen yaklaşık çözümlerin test edilmesinde yardım etmede kullanılmıştır. Tezin ikinci kısmında iki kez dejenere olan denklem için sonlu farklar yöntemi incelenmiştir. Nümerik çözümün gerçek çözüme yakınsaklık problemi de araştırılmıştır. Anahtar Kelimeler : Finite Difference Method, Numerical Solution
In the thesis, a new finite difference algorithms are proposed, which can express all the physical properties of the solution correctly, taking into consideration the properties of nonlinear equations which have some properties such as degeneracy. For this purpose, at first, exact solutions of some equations were found. These solutions will help to test of the approximate solutions obtained by the finite difference method. In the second part of the thesis, finite difference method is investigated for two double degenerate equations. The convergence problem of numerical solution is also researched.
In the thesis, a new finite difference algorithms are proposed, which can express all the physical properties of the solution correctly, taking into consideration the properties of nonlinear equations which have some properties such as degeneracy. For this purpose, at first, exact solutions of some equations were found. These solutions will help to test of the approximate solutions obtained by the finite difference method. In the second part of the thesis, finite difference method is investigated for two double degenerate equations. The convergence problem of numerical solution is also researched.
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Keywords
Matematik, Mathematics
