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On the discrete maximum principle for parabolic difference operators. (English) Zbl 0787.65059
Authors’ summary: We derive a discrete analogue for parabolic difference inequalities of the Krylov maximum principle for parabolic differential inequalities. The result embraces both explicit and implicit difference schemes and extends to the parabolic case our previous work on linear elliptic difference inequalities with random coefficients [Math. Comput. 55, No. 191, 37-53 (1990; Zbl 0716.39005)].

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
39A10 Additive difference equations
35K15 Initial value problems for second-order parabolic equations
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