随机Volterra积分方程强逼近的平衡欧拉方法

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2025-05-21 DOI:10.1016/j.aml.2025.109613

Quanwei Ren, Yanyan He, Jiayi Liu

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引用次数: 0

摘要

这项工作提出了一类新的平衡欧拉方法设计近似随机沃尔泰拉积分方程。这些方法旨在解决显式欧拉方法通常遇到的某些数值不稳定性。从均方意义上推导了所提方案的收敛阶和稳定性特征。此外，对线性均方稳定性进行了全面的分析研究，重点是卷积测试方程。数值实验证明了平衡欧拉格式的稳定性和收敛性。

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Balanced Euler methods for the strong approximation of stochastic Volterra integral equations

This work presents a novel class of balanced Euler methods designed for approximating stochastic Volterra integral equations. These methods aim to address certain numerical instabilities commonly encountered with the explicit Euler approach. The study derives the convergence order and stability characteristics of the proposed schemes in the mean-square sense. Additionally, a comprehensive analytical investigation of linear mean-square stability is provided, focusing on convolution test equations. Numerical experiments highlight the stability and convergence performance of the balanced Euler schemes.

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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.