A random Euler scheme for Carathéodory differential equations

We study a random Euler scheme for the approximation of Carathéodory differential equations and give a precise error analysis. In particular, we show that under weak assumptions, this approximation scheme obtains the same rate of convergence as the classical Monte–Carlo method for integration proble...

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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 224; no. 1; pp. 346 - 359
Main Authors Jentzen, A., Neuenkirch, A.
Format Journal Article
LanguageEnglish
Published Kidlington Elsevier B.V 01.02.2009
Elsevier
Subjects
Acceleration of convergence
Carathéodory differential equations
Error analysis
Euler scheme
Exact sciences and technology
Mathematical analysis
Mathematics
Monte–Carlo methods
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Partial differential equations
Sciences and techniques of general use
Euler scheme
Carathéodory differential equations
Monte–Carlo methods
Euler equation
Monte Carlo method
Approximation
Error analysis
Numerical integration
Error estimation
Convergence acceleration
Differential equation
Stochastic method
Monte-Carlo methods
Convergence
Numerical analysis
Applied mathematics
Convergence rate
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Summary:We study a random Euler scheme for the approximation of Carathéodory differential equations and give a precise error analysis. In particular, we show that under weak assumptions, this approximation scheme obtains the same rate of convergence as the classical Monte–Carlo method for integration problems.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2008.05.060