Approximation of stochastic partial differential equations by a kernel-based collocation method

DOI10.1080/00207160.2012.688111zbMath1269.65006arXiv1108.4213OpenAlexW2136597118MaRDI QIDQ4902864

Gregory E. Fasshauer, Igor Cialenco, Qi Ye

Publication date: 18 January 2013

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1108.4213

zbMATH Keywords

Gaussian processreproducing kernelstochastic partial differential equationimplicit Euler schemeMatérn functionkernel-based collocation

Mathematics Subject Classification ID

Gaussian processes (60G15) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) 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) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22)

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Cites Work

• Reproducing kernels of generalized Sobolev spaces via a Green function approach with distributional operators
• Taylor expansions of solutions of stochastic partial differential equations with additive noise
• Stochastic processes with sample paths in reproducing kernel Hilbert spaces
• Interpolation of spatial data – A stochastic or a deterministic problem?
• A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
• A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
• Solution of stochastic partial differential equations using Galerkin finite element techniques

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