Weak convergence of a numerical method for a stochastic heat equation

Tony Shardlow

doi:10.1023/A:1023661308243

Weak convergence of a numerical method for a stochastic heat equation

Tony Shardlow

Research output: Contribution to journal › Article › peer-review

Abstract

Weak convergence with respect to a space of twice continuously di erentiable test functions is established for a discretisation of a heat equation with homogeneous Dirichlet boundary conditions in one dimension, forced by a space-time Brownian motion. The discretisation is based on finite differences in space and time, incorporating a spectral approximation in space to the Brownian motion.

Original language	English
Pages (from-to)	179-193
Number of pages	14
Journal	BIT Numerical Mathematics
Volume	43
Issue number	1
DOIs	https://doi.org/10.1023/A:1023661308243
Publication status	Published - Mar 2003

Keywords

Initial-boundary value problems
Partial differential equations
Stochastic partial differential equations

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abstract = "Weak convergence with respect to a space of twice continuously di erentiable test functions is established for a discretisation of a heat equation with homogeneous Dirichlet boundary conditions in one dimension, forced by a space-time Brownian motion. The discretisation is based on finite differences in space and time, incorporating a spectral approximation in space to the Brownian motion.",

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AB - Weak convergence with respect to a space of twice continuously di erentiable test functions is established for a discretisation of a heat equation with homogeneous Dirichlet boundary conditions in one dimension, forced by a space-time Brownian motion. The discretisation is based on finite differences in space and time, incorporating a spectral approximation in space to the Brownian motion.

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KW - Partial differential equations

KW - Stochastic partial differential equations

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JO - BIT Numerical Mathematics

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Weak convergence of a numerical method for a stochastic heat equation

Abstract

Keywords

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