LOCAL ERROR-ESTIMATES FOR PARAMETRIZED NONLINEAR EQUATIONS

This paper is concerned with the development of error estimates for parametrized nonlinear equations F(z, lambda ) equals 0 and their discretizations F//h(z, lambda ) equals 0. The estimates obtained are local error estimates in the sense of the local error in the numerical solution of ordinary differential equations. They represent a different approach to the general problem of error estimation, an approach which involves only a single discretized equation instead of a converging family of such equations.