Stochastic diffusion equations are crucial for modeling a range of physical phenomena influenced by uncertainties. We introduce the generalized finite difference method for solving these equations. Then, we examine its consistency, stability and convergence in mean-square, showing that the proposed method preserves stability and demonstrates favorable convergence characteristics under suitable assumptions. In order to validate the methodology, we present numerical results in one-, two-, and three-dimensional space domains.

翻译：随机扩散方程对于模拟受不确定性影响的一系列物理现象至关重要。本文提出了求解此类方程的广义有限差分法。随后，我们在均方意义下分析了该方法的一致性、稳定性与收敛性，结果表明所提方法在适当假设下能保持稳定性，并展现出良好的收敛特性。为验证该方法，我们在一维、二维及三维空间域中给出了数值算例。