The exponential integrator scheme for stochastic partial differential equations: Pathwise error bounds

Journal of Computational and Applied Mathematics

Volumn 235, Issue 5, 2011, Pages 1245-1260

  Kloeden, P E ^a   Lord, G J ^b   Neuenkirch, A ^c   Shardlow, T ^d  

^a GOETHE UNIVERSITY   (Germany)

^b HERIOT WATT UNIVERSITY   (United Kingdom)

^c TU DORTMUND UNIVERSITY   (Germany)

^d UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

Galerkin method; Numerical solution of stochastic PDEs; Pathwise convergence; Stochastic exponential integrator

Indexed keywords

D DIMENSIONS; ERROR BOUND; EXPONENTIAL INTEGRATORS; NUMERICAL SOLUTION; PATHWISE CONVERGENCE; RATE OF CONVERGENCE; SEMILINEAR; STOCHASTIC EVOLUTION EQUATIONS; STOCHASTIC PARTIAL DIFFERENTIAL EQUATION;

APPROXIMATION THEORY; DIFFERENTIAL EQUATIONS; ERROR ANALYSIS; GALERKIN METHODS; STOCHASTIC SYSTEMS;

CONVERGENCE OF NUMERICAL METHODS;

EID: 77957873681     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2010.08.011     Document Type: Article

References (14)

1. G.J. Lord, and J. Rougemont A numerical scheme for stochastic PDEs with Gevrey regularity IMA J. Numer. Anal. 24 2004 587 604
2. G.J. Lord, and T. Shardlow Postprocessing for stochastic parabolic partial differential equations SIAM J. Numer. Anal. 45 2007 870 899
3. I. Gyngy A note on Euler's approximations Potential Anal. 8 1998 205 216
4. P.E. Kloeden, and A. Neuenkirch The pathwise convergence of approximation schemes for stochastic differential equations LMS J. Comput. Math. 10 2007 235 253
5. G.V. Milstein, and M.V. Tretyakov Solving parabolic stochastic partial differential equations via averaging over characteristics Math. Comp. 78 2009 2075 2106
6. I. Gyngy, and D. Nualart Implicit scheme for quasi-linear parabolic partial differential equations perturbed by spacetime white noise Stochastic Process. Appl. 58 1995 57 72
7. I. Gyngy Lattice approximations for stochastic quasi-linear parabolic partial differential equations driven by spacetime white noise I Potential Anal. 9 1998 1 25
8. I. Gyngy Lattice approximations for stochastic quasi-linear parabolic partial differential equations driven by spacetime white noise II Potential Anal. 11 1999 1 37
9. D. Blmker, A. Jentzen, Galerkin approximations for the stochastic Burgers equation, Working Paper, 2010.
10. A. Jentzen Pathwise numerical approximations of SPDEs with additive noise under non-global Lipschitz coefficients Potential Anal. 31 2009 375 404
11. A. Barth, A finite element method for martingale-driven stochastic partial differential equations, COSA (in press).
12. A. Barth, A. Lang, Almost sure convergence of a GalerkinMilstein approximation for stochastic partial differential equations, Working Paper, 2010.
13. A. Pazy Semigroups of Linear Operators and Applications to Partial Differential Equations 1983 Springer-Verlag New York
14. G. Da Prato, and J. Zabczyk Stochastic Equations in Infinite Dimensions 1992 Cambridge University Press Cambridge