带积分边界条件的对流扩散问题弗雷德霍尔积分微分方程数值方法的比较研究

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2024-09-13 DOI:10.1016/j.apnum.2024.09.001

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引用次数: 0

摘要

本文对具有小参数和积分边界条件的弗雷德霍尔积分微分方程进行了数值求解。这些方程的解在右边界有一个边界层。中心差分方案逼近二阶导数，后向差分（上风方案）逼近一阶导数，梯形法则用于积分项和 Shishkin 网格。结果表明，从理论上讲，所提出的方案是均匀收敛的，几乎具有一阶收敛性。为了将收敛阶数从一阶提高到二阶，我们使用了后处理和混合方案。为支持理论结果，我们计算了两个数值示例。

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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A comparative study on numerical methods for Fredholm integro-differential equations of convection-diffusion problem with integral boundary conditions

This paper numerically solves Fredholm integro-differential equations with small parameters and integral boundary conditions. The solution of these equations has a boundary layer at the right boundary. A central difference scheme approximates the second-order derivative, a backward difference (upwind scheme) approximates the first-order derivative, and the trapezoidal rule is used for the integral term with a Shishkin mesh. It is shown that theoretically, the proposed scheme is uniformly convergent with almost first-order convergence. Further to improve the order of convergence from first order to second order, we use the post-processing and the hybrid scheme. Two numerical examples are computed to support the theoretical results.

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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.