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On the worst scenario method: A modified convergence theorem and its application to an uncertain differential equation

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Abstract

We propose a theoretical framework for solving a class of worst scenario problems. The existence of the worst scenario is proved through the convergence of a sequence of approximate worst scenarios. The main convergence theorem modifies and corrects the relevant results already published in literature. The theoretical framework is applied to a particular problem with an uncertain boundary value problem for a nonlinear ordinary differential equation with an uncertain coefficient.

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Authors and Affiliations

  1. Mathematical Institute of the Silesian University in Opava, Na Rybníčku 1, 746 01, Opava, Czech Republic

    Petr Harasim

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  1. Petr Harasim
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Correspondence to Petr Harasim.

Additional information

This research was supported in part by the project MSM4781305904 from the Ministry of Education, Youth and Sports of the Czech Republic.

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Harasim, P. On the worst scenario method: A modified convergence theorem and its application to an uncertain differential equation. Appl Math 53, 583–598 (2008). https://doi.org/10.1007/s10492-008-0043-8

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  • DOI: https://doi.org/10.1007/s10492-008-0043-8

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