Finite Differences Method for One Dimensional Nonlinear Parabolic Equation with Double Nonlinearity

The finite differences scheme for finding a numerical solution of the parabolic equation with double nonlinearity is suggested. For this purpose a special auxiliary problem having some advantages over the main problem is introduced. Some properties of the numerical solution are studied and using the advantages of the proposed auxiliary problem, the convergence of the numerical solution to the exact solution in the sense of mean is proven.