Finite difference approximations for parabolic equations

This master thesis consists of five chapters. In the first chapter, brief information has been given about the studies in other sections.In the second chapter, the fundamental concepts which will be used in the later chapters are presented.In the third chapter,explicit, implicit and the Crank-Nicolson classical finite difference methods are studied for heat conduction problem with various boundary conditions.In the fourth chapter, model problems are considered for heat conduction equation with various boundary conditions. The numerical and analytical solutions are presented in tables.The fifth chapter is the main part of the thesis. This chapter consists of two parts. In the first part, model problems for one-dimensional Burgers? equation are considered and their numerical solutions are obtained for the Predictor-Corrector method and thenthe numerical solutions of problems are comparatively presented with their analytical solutions in tables. In the second part, numerical solutions of the two-dimensional heat equation for the given problem with the Fractional Step Method are obtained and are comparatively presented with their analytical solutions in tables.KEY WORDS: Heat Conduction, The Classical Finite-Difference Methods, Burgers? Equation, Predictor-Corrector(P-C) Method, Alternating Direction Implicit(ADI) Method, Fractional Step(FS) Method