Mesoscopic simulation of Ostwald ripening
Journal of Computational Physics
Wick-stochastic finite element solution of reaction-diffusion problems
Journal of Computational and Applied Mathematics
Noise-induced oscillations in an actively mode-locked laser
Computers & Mathematics with Applications
Finite Element Approximation of the Linear Stochastic Wave Equation with Additive Noise
SIAM Journal on Numerical Analysis
Spatial approximation of stochastic convolutions
Journal of Computational and Applied Mathematics
Higher Order Pathwise Numerical Approximations of SPDEs with Additive Noise
SIAM Journal on Numerical Analysis
Optimal Control of Stochastic Flow over a Backward-Facing Step Using Reduced-Order Modeling
SIAM Journal on Scientific Computing
Delay-dependent stability analysis of numerical methods for stochastic delay differential equations
Journal of Computational and Applied Mathematics
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This paper is concerned with the numerical approximation of some linear stochastic partial differential equations with additive noises. A special representation of the noise is considered, and it is compared with general representations of noises in the infinite dimensional setting. Convergence analysis and error estimates are presented for the numerical solution based on the standard finite difference and finite element methods. The effects of the noises on the accuracy of the approximations are illustrated. Results of the numerical experiments are provided.