DEPENDENCE OF CRITICAL PARAMETER BOUNDS ON THE MONOTONICITY OF A NEWTON SEQUENCE

A new method is proposed for the inclusion of the critical parameter λ* of some convex operator equation u=λTu (appearing e.g. in thermal explosion theory). It is based on the fact that for a fixed λ Newton's method starting with a suitable subsolution is not monotonically if and only if λ>λ*. Several numerical examples arising from nonlinear boundary value problems illustrate the efficiency of the method. © 1979 Springer-Verlag.