Complexity of parametric initial value problems in Banach spaces

Complexity of parametric initial value problems in Banach spaces

We consider initial value problems for parameter dependent ordinary differential equations with values in a Banach space and study their complexity both in the deterministic and the randomized setting, for input data from various smoothness classes. We develop multilevel algorithms, investigate the...

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Veröffentlicht in:Journal of Complexity 2014-08, Vol.30 (4), p.392-429
Hauptverfasser: Daun, Thomas, Heinrich, Stefan
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Banach space
Banach space type
Complexity
Convergence
Differential equations
Initial value problem
Initial value problems
Lower bounds
Multilevel
Multilevel Monte Carlo algorithm
Parametric ordinary differential equation
Smoothness
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Zusammenfassung:We consider initial value problems for parameter dependent ordinary differential equations with values in a Banach space and study their complexity both in the deterministic and the randomized setting, for input data from various smoothness classes. We develop multilevel algorithms, investigate the convergence of their deterministic and stochastic versions, and prove lower bounds.
ISSN:0885-064X
1090-2708
DOI:10.1016/j.jco.2014.01.002