Finite difference schemes for stochastic partial differential equations in Sobolev spaces

DOI10.1007/s00245-014-9272-2zbMath1351.65004arXiv1308.4614OpenAlexW3104696854MaRDI QIDQ496118

Máté Gerencsér, István Gyöngy

Publication date: 17 September 2015

Published in: Applied Mathematics and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1308.4614

zbMATH Keywords

convergenceCauchy problemerror estimationfinite differencesparabolic stochastic partial differential equationsstochastic PDEsextrapolation to the limitRichardson's method\(W_p^m\)-Sobolev space

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) PDEs with randomness, stochastic partial differential equations (35R60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Initial value problems for second-order parabolic equations (35K15)

Related Items (6)

Strong optimal error estimates of discontinuous Galerkin method for multiplicative noise driving nonlinear <scp>SPDEs</scp> ⋮ Localization errors in solving stochastic partial differential equations in the whole space ⋮ Strongly convergent error analysis for a spatially semidiscrete approximation of stochastic partial differential equations with non-globally Lipschitz continuous coefficients ⋮ A Feynman-Kac formula for stochastic Dirichlet problems ⋮ On solvability of integro-differential equations ⋮ On finite difference schemes for partial integro-differential equations of Lévy type

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