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Title: | Numerical Solution of Diffusion Equation in One Dimension |
Authors: | Zangana, Zana Salahaldeen Rashid |
Keywords: | Mathematics Applied Mathematics and Computer Science Mathematical models - Diffusion processes Diffusion Equation, Finite Difference Method, Truncation Error, Stability, Consistency, Convergence |
Issue Date: | Jul-2014 |
Publisher: | Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ) |
Citation: | Zangana, Zana Salahaldeen Rashid. (2014). Numerical Solution of Diffusion Equation in One Dimension. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus. |
Abstract: | ABSTRACT: In this thesis we studied the numerical techniques for the solution of one dimensional diffusion equations. The discrete approximation of the model problem is based on different finite difference schemes. These schemes are the Explicit, Implicit, Crank Nicolson and the Weighted Average schemes. For each finite difference method we studied the local truncation error, consistency and numerical results from the solution of two model problems are considered to evaluate the performance of each scheme according to the accuracy and programming efforts.
Kay word: Diffusion equation, Finite difference method, Truncation error, Stability, Consistency, Convergence.
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ÖZ: Yapılan bu çalışma tek boyutlu difüzyon differansiyel denklem problemlerinin sayısal analiz teknikleri kullanılarak çözülmesi ile ilgilidir. Bu yapılan çalışmada dört farklı sonlu farklar yöntemi problemin çözümü için kullanılmıştır. Dört farklı sonlu farklar yönteminin detaylı olarak nasıl elde edildiği, kesme hataları, stabilite şartları , yoğunluğu ve yakınsamaları detaylı olarak anlatılmıştır. Sonlu farklar metodları iki değişik problem üzerine uygulanmış ve bu metodların karşılaştırılması yapılmıştır.
Anahtar kelimeler: Difüzyon differansiyel denklem, sonlu farklar yöntemleri, kesme hatası, stabilite, yoğunluk ve yakınsama. |
Description: | Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2014. Supervisor: Assoc. Prof. Dr. Derviş Subaşı. |
URI: | http://hdl.handle.net/11129/1674 |
Appears in Collections: | Theses (Master's and Ph.D) – Mathematics
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