A numerical method on a posteriori mesh for a singularly perturbed Riccati equation

IF 2.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2025-09-10 DOI:10.1016/j.apnum.2025.09.003

Zhongdi Cen, Jian Huang, Aimin Xu

引用次数: 0

Abstract

In this paper a singularly perturbed Riccati equation is considered. A hybrid difference method is used to approximate the singularly perturbed Riccati equation. A posteriori error analysis for the discretization method on an arbitrary mesh is given. The stability result of the differential operator used in a posteriori error analysis is obtained based on the properties of the exact solution and the numerical solution. A solution-adaptive algorithm based on a posteriori error estimation is designed to generate a posteriori mesh and the approximation solution. Numerical experiments verify that the method is second-order uniformly convergent with respect to small parameter and improves previous results.

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奇异摄动Riccati方程的后验网格数值解法

本文研究了一类奇异摄动Riccati方程。采用混合差分法逼近奇异摄动Riccati方程。给出了任意网格离散化方法的后验误差分析。基于精确解和数值解的性质，得到了用于后验误差分析的微分算子的稳定性结果。设计了一种基于后验误差估计的解自适应算法来生成后验网格和逼近解。数值实验验证了该方法在小参数下是二阶一致收敛的，改进了以往的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.