Higher order numerical schemes for SPDEs with additive Noise
Numerical Analysis
2025-10-28 v1 Numerical Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.2510.23210,
title = {Higher order numerical schemes for SPDEs with additive Noise},
author = {Abhishek Chaudhary and Andreas Prohl},
journal= {arXiv preprint arXiv:2510.23210},
year = {2025}
}
Comments
14 pages, 2 figures