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NEWTON’S METHOD FOR STOCHASTIC FUNCTIONAL EVOLUTION EQUATIONS IN HILBERT SPACES

Part of: Stochastic analysis Miscellaneous topics - Partial differential equations Numerical methods in calculus of variations and optimal control

Published online by Cambridge University Press:  25 March 2019

Monika Wrzosek
Monika Wrzosek*
Affiliation:
Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland email mwrzosek@mat.ug.edu.pl
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Abstract

We apply Newton’s method to stochastic functional evolution equations in Hilbert spaces using semigroup methods. The first-order convergence is based on our generalization of the Gronwall-type inequality. We also establish a second-order convergence in a probabilistic sense.

MSC classification

Primary: 60H15: Stochastic partial differential equations 35R60: Partial differential equations with randomness, stochastic partial differential equations 49M15: Newton-type methods
Type
Research Article
Information
Mathematika , Volume 65 , Issue 3 , 2019 , pp. 542 - 556
Copyright
Copyright © University College London 2019 

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Footnotes

Supported by grant BW-UG 538-5100-B151-13 from the University of Gdańsk.

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