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     C        are established. The obtained results are generalized for the case of non-uniform spatial grids. Numerical experiments confirming theoretical results are presented.
['Piotr P. Matus', 'Le Minh Hieu', 'Lubin G. Vulkov']
Analysis of second order difference schemes on non-uniform grids for quasilinear parabolic equations