SPURIOUS BEHAVIOR FOR A NUMERICAL SCHEME OF NONLINEAR ELLIPTIC-EQUATIONS

In this paper we investigate finite difference approximations of nonli near elliptic equations of the form Delta u + lambda(u + u(p)) = 0 in three dimensions, where lambda is a positive parameter. We show the ex istence of spurious solution branches, these solutions are spurious in the sense that they are not solutions of the differential problem. We also construct a modified problem describing the behaviour of numeric al solutions, so the finite difference method may be regarded as an ap proximation of the modified problem. We present the results of some nu merical experiments to substantiate our claims. (C) 1995 Academic Pres s, Inc.