Aproximation of Solutions to Nonlinear Equations

Abstract

In this paper we consider the appoximation of solutions to opera tor equations of the form

$$$$

(1)

in a normed linear space with inner product by the Rayleigh-Ritz-Galerkin method. Here A is linear and N nonlinear. In particular we consider two specific questions associated with this approximation:

• (1) When the existence of the Rayleigh-Ritz-Galerkin approximation implies the existence of a solution to (1)

• (2) The calculation of error bounds on the approximation. The method u.,ed to answer these questions is a varient of the Lyapunov-Schmidt or the Alternative method of Cesari.