Higher order numerical schemes for SPDEs with additive Noise
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917045332869120 |
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| author | Chaudhary, Abhishek Prohl, Andreas |
| author_facet | Chaudhary, Abhishek Prohl, Andreas |
| contents | We present high-order numerical schemes for linear stochastic heat and wave equations with Dirichlet boundary conditions, driven by additive noise. Standard Euler schemes for SPDEs are limited to an order convergence between 1/2 and 1 due to the low temporal regularity of noise. For the stochastic heat equation, a modified Crank-Nicolson scheme with proper numerical quadrature rule for the noise term in its reformulation as random PDE achieves a strong convergence rate of 3/2. For the stochastic wave equation with additive noise a corresponding approach leads to a scheme which is of order 2. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_23210 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher order numerical schemes for SPDEs with additive Noise Chaudhary, Abhishek Prohl, Andreas Numerical Analysis We present high-order numerical schemes for linear stochastic heat and wave equations with Dirichlet boundary conditions, driven by additive noise. Standard Euler schemes for SPDEs are limited to an order convergence between 1/2 and 1 due to the low temporal regularity of noise. For the stochastic heat equation, a modified Crank-Nicolson scheme with proper numerical quadrature rule for the noise term in its reformulation as random PDE achieves a strong convergence rate of 3/2. For the stochastic wave equation with additive noise a corresponding approach leads to a scheme which is of order 2. |
| title | Higher order numerical schemes for SPDEs with additive Noise |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2510.23210 |