3 papers
math.NA2026
An hp-version time stepping spectral Monte Carlo method for semi-linear parabolic equations
Jiaying Feng, Zhiyuan Hui, Changtao Sheng +1
In this paper, we present an -version time-stepping spectral Monte Carlo method for solving semi-linear parabolic equations. The key innovation lies in constructing an exponent…
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…
math.NA2025
Exponentially accurate spectral Monte Carlo method for linear PDEs and their error estimates
Jiaying Feng, Changtao Sheng, Chenglong Xu
This paper introduces a spectral Monte Carlo iterative method (SMC) for solving linear Poisson and parabolic equations driven by -stable Lévy process with , which wa…