Burgers denkleminin çözümü için bir yarı-analitik uygulama

Abstract

ÖZET Yüksek Lisans Tezi %85*(56'(1./(0ø1ø1dg=h0hødø1 %ø5<$5,-$1$/ø7ø.8<*8/$0$ Derya TÜRK øQ|Q hQLYHUVLWHVL Fen Bilimleri Enstitüsü 0DWHPDWLN$QDELOLP'DOà 75 + x sayfa 2005 Tez'DQà úPDQà 'Ro'U$OLg='(ù Bu tez yediE|O PGHQROXúPDNWDGà U %LULQFL E|O PGH EX oDOà úPDGD PRGHO SUREOHP RODUDN NXOODQà ODQ %XUJHUV GHQNOHPLKDNNà QGDELOJLYHULOPHNWHGLU øNLQFLE|O PGHNRQX\ODLOJLOLWHPHOWDQà PODUWHRUHPOHUYH\|QWHPOHUNà VDFD WDQà Wà OPDNWDGà U Üçüncü bölümde, 0HWKRI RI /LQHV \|QWHPL Doà NODQDUDN ELU X\JXODPDVà \DSà OPà úWà U Dördüncü bölümde, Burgers denkleminin analitik çözümü verilmektedir. burada, OLQHHUOHúWLULOPLú %HúLQFL E|O P EX oDOà úPDQà Q HVDVà Qà WHúNLO HGLS Burgers denkleminin nümerik çözümleri elGH HGLOPLúWLU $\Uà FD NXOODQà ODQ \|QWHPOHULQNDUDUOà Oà NDQDOL]L\DSà OPà úWà U $OWà QFà E|O P \LQH tezin temelNà VPà ROXS\|QWHPOHUGHQNOHPHGR÷UXGDQ uygulanDUDNQ PHULNo|] POHUHOGHHGLOPLúWLU Yedinci bölümde, elde edilen VRQXoODUà QNDUúà ODúWà Uà OPDVà YHULOPHNWHGLU Burgers denklemi, Method of Lines, Euler yöntemi, $1$+7$5 .(/ø0(/(5 mertebeden ve Dördüncü mertebeden Runge-Kutta yöntemleri, Crank- øNLQFL Nicolson yöntemi, Matris yöntemi.

ABSTRACT M.Sc. Thesis A SEMI-ANALITIC APPLICATION FOR SOLUTION OF BURGERS? EQUATION Derya TÜRK øQ|Q 8QLYHUVLW\ Graduate School of Natural and Applied Sciences Department of Mathematics 75 + x pages 2005 Supervisor : Assoc. Prof. $OLg='(ù This thesis consists of seven chapters. In chapter 1, it is devoted to Burgers? equation that is used as a model problem in this study. In chapter 2, it is briefly introduced general concepts, theorem and methods concerning with the subject. In chapter 3, The Method of Lines is explained and applied to a problem. In chapter 4, equation is given. DQDOLWLFVROXWà RQRI%XUJHUV? Chapter 5 is the main part of this study in which numerical solutions of Burgers? 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, the methods 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.