Solutions of discretized schemes of heat conductionequation via classical finite difference methods byseperation of variables technique

In the rst chapter of this thesis consisting of three chapters, some fundamental information and concepts that will be used in the thesis as well as some substantial information about the classical nite difference and the separation of variables methods frequently encountered in the literature and used for obtaining the approximate and exact solutions of the one-dimensional heat equation given together with the initial and boundary conditions are given. In the second chapter constituting the main body of the thesis, exact (Fourier series) solution has been obtained by the method of separation of variables via the classical nite difference schemes of the one dimensional heat equation subject to two different initial and boundary conditions. In the third chapter, which is the last chapter of the thesis, two test problems have been taken into consideration for one dimensional heat equation. Numerical solutions of each test problem have been obtained by using the classical nite difference schemes as called discretized numerical schemes and the method of separation of variables of these schemes. The obtained numerical results are compared with analytical solution and presented in tables together with the error norms L2 and L1. Moreover, to show the continuity of the obtained results, some graphs have been illustrated.