Finite differences method for one dimensional nonlinear parabolic equation with degeneration

In the thesis, a new finite difference algorithms are proposed, which can express all the physical properties of the solution correctly, taking into consideration the properties of nonlinear equations which have some properties such as degeneracy. For this purpose, at first, exact solutions of some equations were found. These solutions will help to test of the approximate solutions obtained by the finite difference method. In the second part of the thesis, finite difference method is investigated for two double degenerate equations. The convergence problem of numerical solution is also researched.