Accelerated finite difference schemes for stochastic partial differential equations in the whole space

TL;DR

This paper establishes conditions for accelerating the convergence of finite difference schemes for linear stochastic parabolic PDEs in the whole space using Richardson's method, enabling higher-order accuracy in numerical solutions.

Contribution

It introduces sufficient conditions under which Richardson's method can enhance the convergence order of finite difference schemes for stochastic PDEs.

Findings

Convergence can be accelerated to any order with Richardson's method.

Provides sufficient conditions for convergence acceleration.

Applicable to linear stochastic parabolic PDEs in the whole space.

Abstract

We give sufficient conditions under which the convergence of finite difference approximations in the space variable of the solution to the Cauchy problem for linear stochastic PDEs of parabolic type can be accelerated to any given order of convergence by Richardson's method.