A semi-analitic application for solution of Burgers equation

ABSTRACTM.Sc. ThesisA SEMI-ANALITIC APPLICATIONFOR SOLUTION OF BURGERS? EQUATIONDerya TÜRKøQ|Q8QLYHUVLW\Graduate School of Natural and Applied SciencesDepartment of Mathematics75 + x pages2005Supervisor : Assoc. Prof. $OLg='(ùThis thesis consists of seven chapters.In chapter 1, it is devoted to Burgers? equation that is used as a modelproblem in this study.In chapter 2, it is briefly introduced general concepts, theorem and methodsconcerning with the subject.In chapter 3, The Method of Lines is explained and applied to a problem.In chapter 4, equation is given.DQDOLWLFVROXWÕRQRI%XUJHUV?Chapter 5 is the main part of this study in which numerical solutions ofBurgers? equation reduced by the Hopf-Cole transformation are obtained. Also,stability of the methods is investigated.Chapter 6 is also important part of this thesis. In this chapter, themethods are directly applied to Burgers? equation.In chapter 7, it is given the comparison of the obtained numerical solutions.KEYWORDS: Burgers? equation, Method of Lines, Euler method, 2. order and 4.order Runge-Kutta methods, Crank-Nicolson method, Matrix method.