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Constrained Mesh Methods for Functional Differential Equations

  • Chapter
Delay Equations, Approximation and Application

Abstract

Consider the following Volterra Delay Integro Differential Equation (VDIDE):

$$ y'(t) = f(t,y(t),\int\limits_{{t_0}}^t {k(t,s,y(s))ds,y(t - \tau (t)),\int\limits_{{t_0}}^{t - \sigma (t)} {k'} (t,s,y(s))ds} ) $$
((1))

with initial conditions:

$$ \begin{gathered} y({t_0}) = {y_0} \hfill \\ and\quad y(t): = g(t)\quad for\,\;t < {t_0} \hfill \\ \end{gathered} $$

where y: [to,b]→ℝn, f∈[to,b]×ℝ4n→ℝn and both K,K′ map: {(t,s): to≦s≦t≦b} × ℝn→ℝn. Moreover assume the delays τ and σ are continuous and strictly positive. For K=K′=0 (1) reduces to a Delay Differential Equation (DDE), and for τ=σ=0 to a Volterra Integro Differential Equation (VIDE).

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Authors and Affiliations

  1. Istituto di Matematica, Università di Trieste, Italy

    A. Bellen

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  1. A. Bellen
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Editors and Affiliations

  1. Lehrstuhl für Mathematik IV, Universität Mannheim, D-6800, Mannheim 1, Germany

    G. Meinardus

  2. Fakultät für Mathematik und Informatik, Universität Mannheim, D-6800, Mannheim, Germany

    G. Nürnberger

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© 1985 Birkhäuser Verlag Basel

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Bellen, A. (1985). Constrained Mesh Methods for Functional Differential Equations. In: Meinardus, G., Nürnberger, G. (eds) Delay Equations, Approximation and Application. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 74. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7376-5_3

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  • DOI: https://doi.org/10.1007/978-3-0348-7376-5_3

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-7378-9

  • Online ISBN: 978-3-0348-7376-5

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