On the Order of Accuracy for Difference Approximations of Initial–Boundary Value Problems

Finite dierence approximations of the second derivative in space appearing in, parabolic, incompletely parabolic systems of, and second order hyperbolic, partial dierential equations are considered. If the solution is pointwise bounded, we prove that nite dierence approx- imations of those classes of equations can be closed with two orders less accuracy at the boundary without reducing..