A simplified Milstein scheme for SPDEs with multiplicative noise
type: Item
instance of: scholarly article
title: A simplified Milstein scheme for SPDEs with multiplicative noise
zbMATH Open document ID: 1468.60086
DOI: 10.1155/2014/140849
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: This paper deals with a research question raised by \textit{A. Jentzen} and \textit{M. Röckner} [Found. Comput. Math. 15, No. 2, 313--362 (2015; Zbl 1318.60072)], whether the exponential term in their introduced scheme can be replaced by a simpler mollifier. This replacement can lead to more simplification and computational reduction in simulation. So, in this paper, we essentially replace the exponential term with a Padé approximation of order 1 and denote the resulting scheme by simplified Milstein scheme. The convergence analysis for this scheme is carried out and it is shown that even with this replacement the order of convergence is maintained, while the resulting scheme is easier to implement and slightly more efficient computationally. Some numerical tests are given that confirm the order of accuracy and also computational cost reduction.
Mathematics Subject Classification ID: 60H35
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 65N75
zbMATH DE Number: 7021796
author: Bakhtiyar Ghayebi
author: S. Mohammad Hosseini
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/140849
OpenAlex ID: W2094532871
Wikidata QID: Q59035443
cites work: Stochastic Equations in Infinite Dimensions
cites work: Approximation Schemes for Stochastic Differential Equations in Hilbert Space
cites work: On the discretization in time of parabolic stochastic partial differential equations
cites work: Higher-order implicit strong numerical schemes for stochastic differential equations
cites work: Numerical methods for stochastic parabolic PDEs
cites work: An Accelerated Splitting-up Method for Parabolic Equations
cites work: Convergence of numerical schemes for the solution of parabolic stochastic partial differential equations
cites work: Numerical analysis of semilinear stochastic evolution equations in Banach spaces
cites work: Almost sure convergence of a semidiscrete Milstein scheme for SPDEs of Zakai type
cites work: Efficient simulation of nonlinear parabolic SPDEs with additive noise
cites work: Linear-implicit strong schemes for Itô-Galerkin approximations of stochastic PDEs
cites work: Galerkin Finite Element Methods for Stochastic Parabolic Partial Differential Equations
cites work: On numerical solutions of the stochastic wave equation
cites work: Consistency and stability of a Milstein-Galerkin finite element scheme for semilinear SPDE
cites work: A concise course on stochastic partial differential equations
cites work: A Milstein scheme for SPDEs
cites work: Regularity analysis for stochastic partial differential equations with nonlinear multiplicative trace class noise
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description: scientific article; zbMATH DE number 7021796