Positivity-preserving schemes for some nonlinear stochastic PDEs

TL;DR

This paper presents a new numerical scheme that preserves positivity for certain nonlinear stochastic heat equations driven by time-dependent Brownian motion, supported by numerical experiments and convergence analysis.

Contribution

The paper introduces a positivity-preserving numerical scheme for nonlinear stochastic heat equations driven by time-dependent Brownian motion, extending previous work to a different framework.

Findings

The scheme maintains positivity in numerical solutions.

Numerical experiments demonstrate the scheme's effectiveness.

Convergence results confirm theoretical properties.

Abstract

We introduce a positivity-preserving numerical scheme for a class of nonlinear stochastic heat equations driven by a purely time-dependent Brownian motion. The construction is inspired by a recent preprint by the authors where one-dimensional equations driven by space-time white noise are considered. The objective of this paper is to illustrate the properties of the proposed integrators in a different framework, by numerical experiments and by giving convergence results.