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math.NA2025
A derivative-free localized stochastic method for very high-dimensional semilinear parabolic PDEs
Shuixin Fang, Changtao Sheng, Bihao Su +1
We develop a mesh-free, derivative-free, matrix-free, and highly parallel localized stochastic method for high-dimensional semilinear parabolic PDEs. The efficiency of the proposed…
math.NA2025
Numerical Method for Space-Time Fractional Diffusion: A Stochastic Approach
Tengteng Cui, Chengtao Sheng, Bihao Su +1
In this paper, we develop and analyze a stochastic algorithm for solving space-time fractional diffusion models, which are widely used to describe anomalous diffusion dynamics. The…
math.NA2025
Efficient implicit-explicit sparse stochastic method for high dimensional semi-linear nonlocal diffusion equations
Changtao Sheng, Bihao Su, Chenglong Xu
In this paper, we present a sparse grid-based Monte Carlo method for solving high-dimensional semi-linear nonlocal diffusion equations with volume constraints. The nonlocal model i…