Multilevel Picard approximations of high-dimensional semilinear partial differential equations with locally monotone coefficient functions

The full history recursive multilevel Picard approximation method for semilinear parabolic partial differential equations (PDEs) is the only method which provably overcomes the curse of dimensionality for general time horizons if the coefficient functions and the nonlinearity are globally Lipschitz...

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Bibliographic Details
Published in:Applied numerical mathematics Vol. 181; pp. 151 - 175
Main Authors: Hutzenthaler, Martin, Nguyen, Tuan Anh
Format: Journal Article
Language:English
Published: Elsevier B.V 01.11.2022
Subjects:
Curse of dimensionality
High-dimensional PDEs
Locally monotone
Multilevel Monte Carlo method
Multilevel Picard approximations
Tamed Euler-type approximation
Multilevel Picard approximations
Curse of dimensionality
Multilevel Monte Carlo method
Locally monotone
Tamed Euler-type approximation
High-dimensional PDEs
ISSN:0168-9274, 1873-5460
Online Access:Get full text
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Summary:The full history recursive multilevel Picard approximation method for semilinear parabolic partial differential equations (PDEs) is the only method which provably overcomes the curse of dimensionality for general time horizons if the coefficient functions and the nonlinearity are globally Lipschitz continuous and the nonlinearity is gradient-independent. In this article we extend this result to locally monotone coefficient functions. Our results cover a range of semilinear PDEs with polynomial coefficient functions.
ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2022.05.009