基于内核的求解一般分数(整数)-微分-代数方程的新方法

IF 8.7 2区 工程技术 Q1 Mathematics
Tayebeh Taheri, Alireza Afzal Aghaei, Kourosh Parand
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引用次数: 0

摘要

最近推出的用于求解微分方程和积分方程的最小二乘支持向量回归(LS-SVR)算法引发了人们的兴趣。在本研究中,我们扩展了该算法的应用范围,以解决一般形式的微分代数方程(DAE)系统。我们的研究通过在 LS-SVR 机器学习模型、加权残差法和 Legendre 正交多项式之间建立联系,提出了一种以算子格式求解一般 DAE 的新方法。为了评估我们提出的方法的有效性,我们进行了涉及各种 DAE 场景的模拟,如非线性系统、分数阶导数、整微分和偏 DAE。最后,我们将我们提出的方法与目前最先进的方法进行了比较,证明了其可靠性和有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

A new kernel-based approach for solving general fractional (integro)-differential-algebraic equations

A new kernel-based approach for solving general fractional (integro)-differential-algebraic equations

The recent introduction of the Least-Squares Support Vector Regression (LS-SVR) algorithm for solving differential and integral equations has sparked interest. In this study, we extend the application of this algorithm to address systems of differential-algebraic equations (DAEs) in general form. Our work presents a novel approach to solving general DAEs in an operator format by establishing connections between the LS-SVR machine learning model, weighted residual methods, and Legendre orthogonal polynomials. To assess the effectiveness of our proposed method, we conduct simulations involving various DAE scenarios, such as nonlinear systems, fractional-order derivatives, integro-differential, and partial DAEs. Finally, we carry out comparisons between our proposed method and currently established state-of-the-art approaches, demonstrating its reliability and effectiveness.

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来源期刊
Engineering with Computers
Engineering with Computers 工程技术-工程:机械
CiteScore
16.50
自引率
2.30%
发文量
203
审稿时长
9 months
期刊介绍: Engineering with Computers is an international journal dedicated to simulation-based engineering. It features original papers and comprehensive reviews on technologies supporting simulation-based engineering, along with demonstrations of operational simulation-based engineering systems. The journal covers various technical areas such as adaptive simulation techniques, engineering databases, CAD geometry integration, mesh generation, parallel simulation methods, simulation frameworks, user interface technologies, and visualization techniques. It also encompasses a wide range of application areas where engineering technologies are applied, spanning from automotive industry applications to medical device design.
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