基于 BDF 方法的隐式延迟修正方法的稳定性

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED Applied Mathematics Letters Pub Date : 2024-08-03 DOI:10.1016/j.aml.2024.109255

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引用次数: 0

摘要

Dahlquist 障碍指出，A 级稳定线性多步方法的最高阶数限制在 2 阶。本文采用延迟修正方法和 BDF 方法，开发了 A 级稳定的低阶三阶和四阶多步方法。我们对这些方法的稳定性进行了研究，以说明如何实现 A 级稳定性。我们还进行了数值实验，以验证所提方法在应用于刚性问题时的准确性和稳定性。

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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Stability of implicit deferred correction methods based on BDF methods

The Dahlquist barrier states that the highest attainable order for an A-stable linear multistep method is limited to 2. In this paper, we adopt the deferred correction approach with the BDF methods to develop A-stable third and fourth-order multistep methods with low stages. The stability of the methods is investigated to show how A-stability can be achieved. Numerical experiments are conducted to validate the accuracy and stability of the proposed methods when applied to stiff problems.

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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.