| Title:
|
On the worst scenario method: a modified convergence theorem and its application to an uncertain differential equation (English) |
| Author:
|
Harasim, Petr |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
53 |
| Issue:
|
6 |
| Year:
|
2008 |
| Pages:
|
583-598 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
worst scenario problem |
| Keyword:
|
nonlinear differential equation |
| Keyword:
|
uncertain input parameters |
| Keyword:
|
Galerkin approximation |
| MSC:
|
34B15 |
| MSC:
|
47H05 |
| MSC:
|
47J05 |
| MSC:
|
47N20 |
| MSC:
|
65L60 |
| idZBL:
|
Zbl 1199.47207 |
| idMR:
|
MR2469067 |
| DOI:
|
10.1007/s10492-008-0043-8 |
| . |
| Date available:
|
2010-07-20T12:40:54Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140342 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Hlaváček, I.: Reliable solution of elliptic boundary value problems with respect to uncertain data.Nonlinear Anal., Theory Methods Appl. 30 (1997), 3879-3890. MR 1602891, 10.1016/S0362-546X(96)00236-2 |
| Reference:
|
[4] Hlaváček, I., Chleboun, J., Babuška, I.: Uncertain Input Data Problems and the Worst Scenario Method.Elsevier Amsterdam (2004). Zbl 1116.74003, MR 2285091 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| . |
