Zaman içeren problemlerin çözümüne bir nümerik yaklaşım

Abstract

ÖZETYüksek Lisans Tezi=$0$1ød(5(1352%/(0/(5ø1dg=h0h1(%ø51h0(5ø.<$./$ù,0ùXOHKDQ%$ù(5*h9(1øQQÂhQLYHUVLWHVL)HQ%LOLPOHUL(QVWLWÂVÂ0DWHPDWLN$QDELOLP'DOÃ46+vii sayfa2005'DQÃúPDQ'Ro'U$OLg]GHúBirinci bölümde sonraki bölümlerde%X oDOÃúPD EHú EOÂPGHQ ROXúPDNWDGÃUNXOODQÃOPÃúRODQED]ÃWHPHONDYUDPYH/QWHPOHUH/HUYHULOGLbölümde diffusion-FRQYHFWLRQGHQNOHPLWDQÃWÃOGà veGHQNOHPLQELU/DUÃDQDOLWLNøNLQFLçözümü olan piecewise analitik çözümü verildi. Diffusion-convection denkleminin piecewiseçözümü ile DQDOLWLNo]ÂPNDUúÃODúWÃUÃOPDODUÃWDEORODUKDOLQGHVXQXOGXÜçüncü bölümde MOL yöntemiyle diskrize edilen diffusion-convection denklemiEuler ve Runge-Kutta yöntemleri ile çözüldü. Diffusion-convection denkleminin nümerik veanalitik çözümNDUúÃODúWÃUÃOPDODUÃWDEORODUKDOLQGHVXQXOGXDördüncü bölümde Euler ve Runge-Kutta yöntemleri içLQNDUDUOÃOÃNDQDOL]L/DSÃOGÃ%HúLQFL EOÂPGH oDOÃúPDPÃ]GD NXOODQÃODQ /QWHPOHUGHQ HOGH HGLOHQ VRQXoODUGH÷HUOHQGLULOGL: Diffusion-convection denklemi, MOL yöntemi, Euler yöntemi,$1$+7$5.(/ø0(LERRunge-Kutta yöntemi, Piecewise analitik yöntemi

ABSTRACTMaster ThesisA NUMERICAL APPROACH TO PROBLEMSINCLUDING TIMEùXOHKDQ%$ù(5*h9(1Inonu UniversityInstitute of Natural and Applied SciencesMathematics Department46+vii pages2005Supervisor: Assoc. Prof. 'U$OLg]GHúThis study consists of five chapters. Chapter 1 includes some basic concepts andmethods which were used in the latter chapters.In chapter 2, diffusion-convection equation was introduced and piecewise analyticalmethod which is the half-analytical solution of this equation was given. The comparison ofpiecewise analytical solution and analytical solution of diffusion-convection equation werepresented in the tables.In chapter 3, diffusion-convection equation which we obtained by discreazing withMOL method was solved with Euler and Runge-Kutta methods. The comparison of numericaland 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 methodi