CLASSICAL AND NUMERICAL SOLUTIONS OF THE VISCOUS BURGERS EQUATION

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2023-1-11

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Koşar, Melisa

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In this study, the viscous Burgers equation is studied both theoretically and numerically. Before introducing our model of interest, we provide a brief historical concept of the equation where we also remind the reader some basic concepts of the partial differential equations. Here the linear advection equation, the solution of which is a particular case of first order quasilinear partial differential equations, is taken into account as an example. The solutions of the inviscid Burgers equation follows by similar process. The main part of this thesis is devoted to the solutions by utilizing the Hopf-Cole transform. In the next part, the model is investigated by implementation of numerical techniques. We used Backward Time Centered Space (BTCS) and Forward Time Centered Space (FTCS) for the numerical results. Comparison of analytical and numerical results and error analysis are described for several examples on the final part of that work.

Subject Keywords

Hopf-Cole transformation, Method of Separation of Variables, Finite Difference Method, Viscous Burgers equation,

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https://hdl.handle.net/11511/101917

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Graduate School of Natural and Applied Sciences, Thesis

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Citation Formats

M. Koşar, “CLASSICAL AND NUMERICAL SOLUTIONS OF THE VISCOUS BURGERS EQUATION,” M.S. - Master of Science, Middle East Technical University, 2023.