Die maximale Konsistenzordnung von Differenzenapproximationen nichtnegativer Art (Q792076)

The differential operator \[ (Ly)(x)=- \sum^{N}_{i,j=1}a_{ij}(x)(D_ iD_ jy)(x)+\sum^{N}_{i=1}a_ i(x)(D_ iy)(x)+a(x)y(x),x\in {\mathbb{R}}^ n \] is discretized by a set of difference operators \((L_ hy)(x)=-h^{-2}a_ 0(x,h)y(x)-h^{- 2}\sum^{m}_{k=1}a_ k(x,h)y(x+c_ kh).\) If L is elliptic in \(x=x_ 0\) and if \(a_ k(x_ 0,h)\geq 0\), \(0<h\leq h_ 0\), \(k=1,...,m\), it is shown, that \(L_ h\) is at most consistent of order two to L.