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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
Explicit Runge-Kutta schemes for Backward Stochastic Differential Equations
Shuixin Fang, Yue Qiu, Weidong Zhao
The Butcher theory provides a powerful tool for analyzing order conditions of Runge-Kutta schemes for ordinary differential equations (ODEs); however, such a theory has not yet bee…
math.NA2025
Deep random difference method for high-dimensional quasilinear parabolic partial differential equations
Wei Cai, Shuixin Fang, Tao Zhou
Solving high-dimensional parabolic partial differential equations (PDEs) with deep learning methods is often computationally and memory intensive, primarily due to the need for aut…