A splitting/polynomial chaos expansion approach for stochastic evolution equations
Provides a new computational method for stochastic PDEs, relevant to researchers in numerical analysis and stochastic modeling.
The paper combines deterministic splitting methods with polynomial chaos expansion to solve stochastic parabolic evolution equations, reducing them to deterministic systems. Numerical experiments validate the approach with convergence analysis.
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.