On the iterative solutions of some nonlinear eigenvalue problems
Kazimierz Wanelik · Journal of Mathematical Physics · 1989
A simple refinement procedure of iteration methods for nonlinear systems is presented. It is based upon the introduction of a numerical measure of the ‘‘separation’’ between iterates, which themselves depend on parameters to be determined by requirements on the magnitude of this ‘‘separation.’’ As a simple but informative application of this idea the refined Picard iteration of the null Dirichlet problem for Δu+λf (x,u)=0 is considered. To illustrate the use of this technique the equation of Bratu and the so-called Gel’fand problem is observed. A discussion follows.