We introduce and analyze an explicit time discretization scheme for the one-dimensional
stochastic Allen-Cahn, driven by space-time white noise. The scheme is based on a splitting …

This article proposes and analyzes explicit and easily implementable temporal numerical
approximation schemes for additive noise-driven stochastic partial differential equations …

A fully discrete approximation of the semilinear stochastic wave equation driven by
multiplicative noise is presented. A standard linear finite element approximation is used in …

This article introduces a certain class of stochastic processes, which we suggest calling mild
Itô processes, and a new, somehow mild, Itô-type formula for such processes. Examples of …

The time integration of stiff systems of Ordinary Differential Equations (ODEs), usually arising
from the spatial discretization of Partial Differential Equations (PDEs), constitutes a hot topic …

A fully discrete approximation of the one-dimensional stochastic heat equation driven by
multiplicative space–time white noise is presented. The standard finite difference …

The aim of this article is to provide further strong convergence results for a spatio-temporal
discretization of semilinear parabolic stochastic partial differential equations driven by …

Including the effect of thermal fluctuations in traditional computational fluid dynamics
requires developing numerical techniques for solving the stochastic partial differential …

In this article, we propose an algorithm for approximating the action of φ− functions of
matrices against vectors, which is a key operation in exponential time integrators. In …

This work is devoted to convergence analysis of an exponential integrator scheme for semi-
discretization in time of nonlinear stochastic wave equation. A unified framework is first set …