# A splitting/polynomial chaos expansion approach for stochastic evolution equations

## TL;DR

This paper introduces a novel approach combining splitting methods with polynomial chaos expansion to efficiently solve stochastic evolution equations, supported by convergence analysis and numerical validation.

## Contribution

It develops a new method integrating deterministic splitting with polynomial chaos for stochastic PDEs, enhancing solution efficiency and accuracy.

## Key findings

- Method effectively reduces stochastic PDEs to deterministic systems.
- Convergence analysis confirms the method's reliability.
- Numerical experiments validate the approach's accuracy.

## Abstract

In this paper, we combine deterministic splitting methods with a polynomial chaos expansion method for solving stochastic parabolic evolution problems. The stochastic differential equation is reduced to a system of deterministic equations that we solve explicitly by splitting methods. The method can be applied to a wide class of problems where the related stochastic processes are given uniquely in terms of stochastic polynomials. A comprehensive convergence analysis is provided and numerical experiments validate our approach.