Master Degree / Yüksek Lisans Tezleri
Permanent URI for this collectionhttps://hdl.handle.net/11147/3008
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Master Thesis A Comparison of Meshless and Finite Difference Methods for the Brusselator Model(Izmir Institute of Technology, 2022) Tanoğlu, Gamze; Tanoğlu, Gamze; Tanoğlu, Gamze; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyThe purpose of this thesis is the Brusselator model, which is used to model the reaction-diffusion occurring in processes of a chemical such as the formation of turing patterns in the skin of an animal, enzymatic reaction, ozone formation through triple collision with atomic oxygen; using methods such as Meshless Method and Finite Difference Method in space discretization and Runge Kutta Method, and the Adaptive Runge Kutta Method in time discretization, to find the method that gives more accurate. It is also to estimate the degree of the Meshless Method using the Finite Difference Method.Master Thesis Computation of the Convection Diffusion Equation by the Fourth Order Compact Finite Difference Method(Izmir Institute of Technology, 2015) Bajellan, Asan Ali Akbar Fatah; Tayfur, Gökmen; Tayfur, Gökmen; 03.03. Department of Civil Engineering; 03. Faculty of Engineering; 01. Izmir Institute of TechnologyThis dissertation aims to develop various numerical techniques for solving the one dimensional convection–diffusion equation with constant coefficient. These techniques are based on the explicit finite difference approximations using second, third and fourth-order compact difference schemes in space and a first-order explicit scheme in time. The suggested scheme has been seen to be very accurate and a relatively flexible solution approach in solving the contaminant transport equation for Pe ≤ 5. For the solution, the combined technique has been used instead of conventional solution techniques. The accuracy and validity of the numerical model are verified. The computed results showed that the use of the current method in the simulation is very applicable for the solution of the convection-diffusion equation. The technique is seen to be alternative to existing techniques. This dissertation is divided into six chapters: The derivation of the convective diffusion equation is given in Chapter 2. The main idea behind the higher order finite difference technique is given in Chapter 3. The numerical approximations to CDE described with ten different explicit schemes are introduced in Chapter 4. The results of numerical experiments using second, third and fourth-order compact difference schemes are presented in Chapter 5. Chapter 6 is devoted to a brief conclusion. Finally the references are introduced at the end.