2024/11/21 by Mojarrad, Faezeh Nassajian
#FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2411.14333
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.