LINEAR-IMPLICIT STRONG SCHEMES FOR ITO-GALKERIN APPROXIMATIONS OF STOCHASTIC PDES

By Peter E. Kloeden, S. Shott. 2001

64 citations recorded by the source corpus.

Linear-implicit versions of strong Taylor numerical schemes for finite dimensional Itô stochastic differential equations (SDEs) are shown to have the same order as the original scheme. The combined truncation and global discretization error of an γ strong linear-implicit Taylor scheme with time-step Δ applied to the N dimensional Itô-Galerkin SDE for a class of parabolic stochastic partial differential equation (SPDE) with a strongly monotone linear operator with eigenvalues λ1≤λ2≤… in its drift term is then estimated by K(λN

Subfields: Computational Mechanics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/ffb5ae91366727e0a1e1a1d22250a41b5e2ed994

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In Computational Mechanics

In Numerical Analysis

Citations in the corpus

The Numerical Approximation of Stochastic Partial Differential Equations (2009, background): “Kloeden & Shott [ 77 ] showed that for a linear-implicit strong order γ 212 A. Jentzen and P.E.”
A numerical scheme for stochastic PDEs with Gevrey regularity (2004, methodology): “Strong convergence for the implicit Euler–Maruyama scheme has been considered for Galerkin approximations of SPDEs by [8] (who also examines other discretisations in space and time) and in [11].”
Approximation for Semilinear Stochastic Evolution Equations (2003, unknown): “, [16], or [22]).”
Semidiscrete Galerkin Approximation for a Linear Stochastic Parabolic Partial Differential Equation Driven by an Additive Noise (2004, background): “Further contributions include Allen, Novosel and Zhang [1], Benth and Gjerde [2], Davie and Gaines [8], Du and Zhang [10], Gy¨ ongy [13, 14], Hausenblas [16, 17], Kloeden and Shott [ 18 ], Lord and Rougemont [19], Printems [23], Shardlow [24], Theting [25, 26], Yan [29], etc.”
A mild Itô formula for SPDEs (2010, methodology): “In the sequel this is illustrated for Milstein type approximations for SPDEs (see [34, 60, 80, 71, 56, 3, 2, 107, 5]).”
Numerical analysis of semilinear stochastic evolution equations in Banach spaces (2002, background): “; An =(aij)ij; with entries aij = ij9i (see also Greksch and Kloeden [18] and Kloeden and Short [23]).”
Overcoming the order barrier in the numerical approximation of stochastic partial differential equations with additive space–time noise (2009, methodology): “Grecksch & Kloeden (1996) considered a parabolic SPDE driven by a (possibly multiplicative) scalar Wiener process and applied explicit Itô–Taylor schemes (see Kloeden & Platen 1992) to the Galerkin SDEs, while Kloeden & Shott (2001) applied linear-implicit Itô–Taylor schemes to the Galerkin SDEs.”