Abstract
We present here the discretization by a finite-volume scheme of a heat equation perturbed by a multiplicative noise of Itô type and under homogeneous Neumann boundary conditions. The idea is to adapt well-known methods in the deterministic case for the approximation of parabolic problems to our stochastic PDE. In this paper, we try to highlight difficulties brought by the stochastic perturbation in the adaptation of these deterministic tools.
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Bauzet, C., Nabet, F. (2020). Convergence of a Finite-Volume Scheme for a Heat Equation with a Multiplicative Stochastic Force. In: Klöfkorn, R., Keilegavlen, E., Radu, F.A., Fuhrmann, J. (eds) Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples. FVCA 2020. Springer Proceedings in Mathematics & Statistics, vol 323. Springer, Cham. https://doi.org/10.1007/978-3-030-43651-3_24
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DOI: https://doi.org/10.1007/978-3-030-43651-3_24
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