Condition of Differential and Difference Systems
by
Ray Zahar
University of Montreal, Canada

The sensitivity of two-point boundary value problems in linear differential and linear difference systems is discussed. We consider perturbations in all the data, including the defining matrices, and develop measurable algebraic bounds for the relative errors in the individual vectors of the desired solution. Our analysis, which is based on the concept of matrizant for the variation-of-parameters equation, applies uniformly to both differential and difference systems, thus maintaining any existing isomorphism between the fundamental solutions of the two types of equations. The theory is illustrated for the numerical solution of differential equations by series expansions.

Date received: June 7, 1998