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

  • H.-J. Reinhardt
Part of the Applied Mathematical Sciences book series (AMS, volume 57)


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.


Convergence Property Uniform Boundedness Convergence Theory Consistency Sequence Inhomogeneous Problem 
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References (cf. also References in Chapter 4)

  1. Ansorge (1978), von Dein (1976)*, John (1982), Kreth (1975)*, Meis & Marcowitz (1981), Reinhardt (1975a,1975b,1977)*, Richtmyer & Morton (1967), Stetter (1973), Törnig (1979).Google Scholar

Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • H.-J. Reinhardt
    • 1
  1. 1.Fachbereich MathematikJohann-Wolfgang-Goethe-Universität6000 Frankfurt MainFederal Republic of Germany

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