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An interval method for systems of ode

  • S. Markov
  • R. Angelov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 212)

Abstract

Considered is an interval algorithm producing bounds for the solution of the initial value problem for systems of ordinary differential equations \(\dot x(t) = f(t,c,x(t))\), x(to)=xo, involving inexact data c, xo, taking values in given intervals \(C = [\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{c} ,\bar c]\), resp. \(X_o = [\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{x} _o ,\bar x_o ]\). An estimate for the width of the computed inclusion of the solution set is given under the assumption that f is Lipschitzian. In addition, if f is quasi-isotone, the computed bounds converge to the interval hull of the solution set and the order of global convergence is O(h).

Keywords

Nonnegative Integer Global Convergence Iteration Procedure Interval Method Computer Arithmetic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    R.E.Moore.Methods and Applications of Interval Analysis. SIAM Studies in Applied Mathematics. 1979.Google Scholar
  2. 2.
    W.Walter.Differential and Integral Inequalities. Springer, 1970.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • S. Markov
    • 1
    • 2
  • R. Angelov
    • 1
    • 2
  1. 1.Bulgarian Academy of SciencesSofia
  2. 2.High Institute for EconomicsVarnaBulgaria

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