Weak Convergence of a Numerical Method for a Stochastic Heat Equation |
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Authors: | Tony Shardlow |
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Institution: | (1) Department of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, UK |
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Abstract: | Weak convergence with respect to a space of twice continuously differentiable 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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Keywords: | Partial differential equations initial-boundary value problems stochastic partial differential equations |
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