A new ?walk on spheres? type method for fractional diffusion equation in high dimensions based on the Feynman-Kac formulas

被引：0
|
作者：
Su, Bihao [1 ]
Xu, Chenglong [1 ]
Sheng, Changtao [1 ]
机构：
[1] Shanghai Univ Finance & Econ, Sch Math, Shanghai 200433, Peoples R China
来源：
APPLIED MATHEMATICS LETTERS | 2023年 / 141卷
基金：
中国国家自然科学基金;
关键词：
Integral fractional Laplacian; Transition density; Poisson kernel; Monte Carlo method; LAPLACIAN; DYNAMICS; GUIDE;
D O I：
10.1016/j.aml.2023.108597
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we introduce an efficient stochastic method for solving space -fractional diffusion equations in high dimensions based on the Feynman-Kac formula. The key idea is to approximate the trajectory of the process by using a series of balls. As an extension of our first work Sheng et al. (2022) for the Poisson equation, the new algorithm finds remarkably efficient in solving time-dependent linear problems with integral fractional Laplacian on the bounded and unbounded domains. We present some numerical examples to validate the robustness and efficiency of our methods.(c) 2023 Elsevier Ltd. All rights reserved.
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