求解变系数对流扩散方程的legende模型降阶方法

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2025-09-28 DOI:10.1016/j.aml.2025.109773

Zhiyuan Xing , Yanpeng Li , Xiufang Feng , Yaolin Jiang

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引用次数: 0

摘要

本文提出了一种基于移位勒让德多项式的变系数对流扩散方程模型降阶方法。采用有限元离散方法得到了对流扩散方程的常微分方程组。然后，通过位移勒让德多项式逼近系统状态，得到可有效求解的降阶系统，得到数值解。给出了误差分析，并用数值算例验证了所提方法的可行性。

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Legendre-based model order reduction method for solving convection–diffusion equations with variable coefficients

A model order reduction method based on shifted Legendre polynomials for solving convection–diffusion equations with variable coefficients is presented in this paper. The ordinary differential system of the convection–diffusion equation is obtained by finite element discretization procedure. Then, approximating the system state via shifted Legendre polynomials, the reduced-order system is produced, which can be solved efficiently to obtain the numerical solution. Error analysis is presented, and numerical examples are used to verify the feasibility of the presented method.

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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.