A numerical approach to problems including time

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