一类分数阶Allen-Cahn方程的高阶分时蒙特卡罗方法

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2025-01-21 DOI:10.1016/j.aml.2025.109467

Huifang Yuan , Zhiyuan Hui

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引用次数: 0

摘要

在本文中，我们引入了一类适合于分数阶和经典Allen-Cahn方程的新颖的高阶分时蒙特卡罗方法。该方法将谱蒙特卡罗方法（SMC）与时间分裂方案相结合，在谱蒙特卡罗方法有效计算线性传播量和显式计算非线性传播量之间交替进行。对于各种α∈(0,2)的数值结果表明，该方法能够达到一阶、二阶和四阶收敛速率，从而证实了其有效性和准确性。

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

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

α \in (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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来源期刊

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.