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Inclusion theorems for solutions of differential equations with aid of pointwise or vector monotonicity

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Ordinary Differential Equations and Operators

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1032))

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Abstract

This survey describes briefly some methods which use ideas of monotonicity for numerical solution of differential equations. In many cases the approximation methods combined with principles of monotonicity are the only ones which give lower and upper bounds for the wanted solutions. Numerical examples are given for linear and nonlinear partial differential equations and integral equations mostly connected with applications in science. The idea of vector-monotonicity can be used for calculating also derivatives of wanted solutions in not too complicated cases.

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Authors and Affiliations

  1. Institut für Angewandte Mathematik, Bundesstraße 55, 2000, Hamburg 13, Germany

    Prof. Dr. Lothar Collatz

Authors
  1. Prof. Dr. Lothar Collatz
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Editor information

W. N. Everitt R. T. Lewis

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© 1983 Springer-Verlag

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Collatz, L. (1983). Inclusion theorems for solutions of differential equations with aid of pointwise or vector monotonicity. In: Everitt, W.N., Lewis, R.T. (eds) Ordinary Differential Equations and Operators. Lecture Notes in Mathematics, vol 1032. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076794

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  • DOI: https://doi.org/10.1007/BFb0076794

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  • Print ISBN: 978-3-540-12702-4

  • Online ISBN: 978-3-540-38689-6

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