MONOTONIC DIFFERENCE SCEEMES FOR ELLIPTIC AND.PARABOLIC EQUATIONS IN THE CASE OF A NON-SELFADJOINT ELLIPTIC OPERATOR *

THE present note ProDoses monotonic schemes. uniformly convergent at a rate 0(h2), for a non-selfadjofnt second order elliptic equation in an arbitrary region, and also monotonic locally one-dimensional schemes, uniformly convergent at a rate 0(h2 + T) for a parabolic equation with non-selfadjoint elliptic operator. 1. le take the first boundary value problem in the domain G i r of p-dimensional space x = (xl,..., *,I for an elliptic equation contain-ing first derivatives Lu=-f, XEG, BIF = fl, 0) where k, = k,f=) 2 Cl> 0, n=g(rf3*0,r==r=(zf, f=f(s), f,=f*(q,c,=kd cl is a constant. We consider as usual a mesh oh(G) in the region G, formed by the intersection of the hy9ernlanes I.. = i,h,, icr = 0, fl, AZ,.... a = i,..,, p, where ho is the interval of the mesh; the base-points Xi = (ilhl..... iphp) E G are interior. the boundary yh of the mesh 0 % consists of the points of intersection of the hyperplanes xo = i,ha with the boundary r of G. The set ah * of interior base-points adjacent to the base-points %i E Yh will be termed the boundary zone, and the set $, of remaining base-points the fundamental region of the mesh