SPURIOUS BEHAVIOR FOR A NUMERICAL SCHEME OF NONLINEAR ELLIPTIC EQUATIONS

摘要

In this paper we investigate finite difference approximations of nonlinear elliptic equations of the form Delta u + lambda(u + u(p)) = 0 in three dimensions, where lambda is a positive parameter. We show the existence 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 numerical solutions, so the finite difference method may be regarded as an approximation of the modified problem. We present the results of some numerical experiments to substantiate our claims. (C) 1995 Academic Press, Inc. [References: 26]