ÖZET Yüksek Lisans Tezi =$0$1ød(5(1352%/(0/(5ø1dg=h0h1( %ø51h0(5ø.<$./$ù,0 ùXOHKDQ%$ù(5*h9(1 øQ|Q hQLYHUVLWHVL)HQ%LOLPOHUL(QVWLW V 0DWHPDWLN$QDELOLP'DOà 46+vii sayfa 2005 'DQà úPDQ'Ro'U$OLg]GHú Birinci bölümde sonraki bölümlerde %X oDOà úPD EHú E|O PGHQ ROXúPDNWDGà U NXOODQà OPà úRODQED]à WHPHONDYUDPYH\|QWHPOHUH\HUYHULOGL bölümde diffusion-FRQYHFWLRQGHQNOHPLWDQà Wà OGà veGHQNOHPLQELU\DUà DQDOLWLN øNLQFL çözümü olan piecewise analitik çözümü verildi. Diffusion-convection denkleminin piecewise çözümü ile DQDOLWLNo|] PNDUúà ODúWà Uà OPDODUà WDEORODUKDOLQGHVXQXOGX Üçüncü bölümde MOL yöntemiyle diskrize edilen diffusion-convection denklemi Euler ve Runge-Kutta yöntemleri ile çözüldü. Diffusion-convection denkleminin nümerik ve analitik çözümNDUúà ODúWà Uà OPDODUà WDEORODUKDOLQGHVXQXOGX Dördüncü bölümde Euler ve Runge-Kutta yöntemleri içLQNDUDUOà Oà NDQDOL]L\DSà OGà %HúLQFL E|O PGH oDOà úPDPà ]GD NXOODQà ODQ \|QWHPOHUGHQ HOGH HGLOHQ VRQXoODU GH÷HUOHQGLULOGL : Diffusion-convection denklemi, MOL yöntemi, Euler yöntemi, $1$+7$5.(/ø0(LER Runge-Kutta yöntemi, Piecewise analitik yöntem i
ABSTRACT Master Thesis A NUMERICAL APPROACH TO PROBLEMS INCLUDING TIME ùXOHKDQ%$ù(5*h9(1 Inonu University Institute of Natural and Applied Sciences Mathematics Department 46+vii pages 2005 Supervisor: Assoc. Prof. 'U$OLg]GHú This study consists of five chapters. Chapter 1 includes some basic concepts and methods which were used in the latter chapters. In chapter 2, diffusion-convection equation was introduced and piecewise analytical method which is the half-analytical solution of this equation was given. The comparison of piecewise analytical solution and analytical solution of diffusion-convection equation were presented in the tables. In chapter 3, diffusion-convection equation which we obtained by discreazing with MOL method was solved with Euler and Runge-Kutta methods. The comparison of numerical and analytical solution of diffusion-convection equation were presented in the tables. In chapter 4, stability analysis for Euler and Runge-Kutta methods was made. In chapter 5, the results obtained by the methods used in this study were evaluated. KEYWORDS: Diffusion-convection equation, The method of lines (MOL), Euler method, Runge-Kutta method, Piecewise analytical method i
