QUALITATIVE PROPERTIES OF THE NUMERICAL-SOLUTION OF LINEAR PARABOLIC PROBLEMS WITH NONHOMOGENEOUS BOUNDARY-CONDITIONS

In papers [1-3], we have formulated the conditions of the conservation of the main characteristic properties of the continuous problem to th e numerical schemes in the case of homogeneous boundary conditions. Su ch properties are the conservation of the nonnegativity and the concav ity of the initial function, monotonicity in time (contractivity) and others. In this paper, we consider similar questions to the problem wi th nonhomogeneous boundary conditions. We analyse the behaviour of the numerical solution in the limit by the time variable on some fixed me sh. We also consider the condition of the preservation of the nonnegat ivity and convexity (concavity) of the initial function. Finally, we e xamine the condition of the conservation of the monotonicity in the sp ace variable of the initial function to the numerical solution.