Inverse Stability and Convergence for General Discrete-Time Approximations of Linear and Nonlinear Initial Value Problems

Abstract

In this chapter, we develop a convergence theory for discrete-time approximations to both linear and nonlinear initial value problems. We shall assume that such problems are pure initial value problems, and allow that the mappings occurring in both the exact formulation of the problem, and in the associated approximations, depend on time. Our convergence theory established for the problems in this chapter will essentially consist of a rather concrete description and characterization of the concepts of inverse stability, consistency, and discrete convergence. These concepts were discussed at length in the development of our general convergence theory in Part II.