CONSISTENT TWO-SIDED ESTIMATES FOR THE SOLUTIONS OF HOMOGENEOUS QUASI-LINEAR PARABOLIC EQUATIONS AND THEIR APPROXIMATIONS
Abstract
In this article, for the linearized difference scheme that approximates the Dirichlet problem for the homogeneous multidimensional quasi-linear parabolic equation with unbounded nonlinearity, two-sided point-wise estimates of the solution are established which are fully consistent with the same estimates for the differential problem. It is interesting to note that the proved two-sided estimates do not depend on diffusion coefficient. The direct application of such estimates is the proof of the convergence of the considered difference scheme in the grid norm L2 . An example of the calculation by the Crank–Nicolson difference scheme is given, showing that the violation of the consistency conditions of differential and difference estimates leads to non-monotonic numerical solutions.
About the Author
D. B. Poliakov
Institute of Mathematics of the National Academy of Sciences of Belarus, Minsk
Belarus
Ph. D. (Physics and Mathematics), Researcher
Belarus
Ph. D. (Physics and Mathematics), Researcher
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