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

Petr Harasim

Applications of Mathematics (2008)

  • Volume: 53, Issue: 6, page 583-598
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Harasim, Petr. "On the worst scenario method: a modified convergence theorem and its application to an uncertain differential equation." Applications of Mathematics 53.6 (2008): 583-598. <http://eudml.org/doc/37802>.

@article{Harasim2008,
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.},
author = {Harasim, Petr},
journal = {Applications of Mathematics},
keywords = {worst scenario problem; nonlinear differential equation; uncertain input parameters; Galerkin approximation; worst scenario problem; nonlinear differential equation; uncertain input parameters; Galerkin approximation},
language = {eng},
number = {6},
pages = {583-598},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the worst scenario method: a modified convergence theorem and its application to an uncertain differential equation},
url = {http://eudml.org/doc/37802},
volume = {53},
year = {2008},
}

TY - JOUR
AU - Harasim, Petr
TI - On the worst scenario method: a modified convergence theorem and its application to an uncertain differential equation
JO - Applications of Mathematics
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 6
SP - 583
EP - 598
AB - 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.
LA - eng
KW - worst scenario problem; nonlinear differential equation; uncertain input parameters; Galerkin approximation; worst scenario problem; nonlinear differential equation; uncertain input parameters; Galerkin approximation
UR - http://eudml.org/doc/37802
ER -

References

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  4. Hlaváček, I., Chleboun, J., Babuška, I., Uncertain Input Data Problems and the Worst Scenario Method, Elsevier Amsterdam (2004). (2004) Zbl1116.74003MR2285091
  5. Hlaváček, I., Křížek, M., Malý, J., 10.1006/jmaa.1994.1192, J. Math. Anal. Appl. 184 (1994), 168-189. (1994) MR1275952DOI10.1006/jmaa.1994.1192
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  7. Chleboun, J., 10.1016/S0362-546X(99)00274-6, Nonlinear Anal., Theory Methods Appl. 44 (2001), 375-388. (2001) Zbl1002.35041MR1817101DOI10.1016/S0362-546X(99)00274-6
  8. Křížek, M., Neittaanmäki, P., Finite Element Approximation of Variational Problems and Applications, Longman Scientific & Technical New York (1990). (1990) MR1066462
  9. Zeidler, E., Applied Functional Analysis. Applications to Mathematical Physics, Springer Berlin (1995). (1995) Zbl0834.46002MR1347691
  10. Zeidler, E., Applied Functional Analysis. Main Principles and Their Applications, Springer New York (1995). (1995) Zbl0834.46003MR1347692

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