A class of higher-order time-splitting Monte Carlo method for fractional Allen-Cahn equation

被引：0
作者：
Yuan, Huifang [1 ]
Hui, Zhiyuan [2 ]
机构：
[1] Harbin Inst Technol, Sch Sci, Shenzhen 518055, Guangdong, Peoples R China
[2] Shanghai Univ Finance & Econ, Sch Math, Shanghai 200433, Peoples R China
来源：
APPLIED MATHEMATICS LETTERS | 2025年 / 163卷
基金：
中国国家自然科学基金;
关键词：
Spectral Monte Carlo method; Time-splitting scheme; Fractional Allen-Cahn equation; Generalized Jacobi function; SCHEME;
D O I：
10.1016/j.aml.2025.109467
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we introduce a novel class of higher-order time-splitting Monte Carlo method tailored for both fractional and classical Allen-Cahn equations. The proposed method integrates the spectral Monte Carlo method (SMC) with a time-splitting scheme, alternating between efficiently computing the linear propagator via the spectral Monte Carlo method and explicitly evaluating the nonlinear propagator. Numerical results for various a is an element of (0, 2] demonstrate the method's ability to achieve first-, second-, and fourth-order convergence rates, thereby confirming its effectiveness and accuracy.
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