Analysis of second order difference schemes on non-uniform grids for quasilinear parabolic equations

On the base of the maximum principles two-sided estimates for solutions of difference schemes are proved without any assumption of sign-definiteness of input data. Second order unconditional monotone difference scheme for quasilinear convection-diffusion equation on uniform grids is constructed. A priori estimates of the difference solution on uniform norm C are established. The obtained results are generalized for the case of non-uniform spatial grids. Numerical experiments confirming theoretical results are presented.