A kernel function based regularized method for boundary value problems with noisy information

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2025-02-01 DOI:10.1016/j.aml.2025.109481

X.L. Li , F.Z. Geng , Y.Q. Gao

引用次数: 0

Abstract

Taking advantage of the reproducing kernel theory, several effective numerical algorithms have been developed to solve boundary value problems (BVPs) with the exact right side functions. However, these methods have difficulty in solving effectively linear boundary value problems when the right side of the equation has contaminated data. The objective of this letter is to introduce a robust numerical algorithm for linear BVPs with noisy right-hand side functions information. To overcome the challenges of the noisy right-hand side functions, the idea of regularization is used. Numerical simulation is employed to illustrate the superiority of the present method.

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一种基于核函数的带噪声边值问题正则化方法

利用再现核理论，开发了几种有效的数值算法来求解具有精确右侧函数的边值问题。然而，当方程右侧有污染数据时，这些方法难以有效地求解线性边值问题。这封信的目的是介绍一个鲁棒的数值算法线性bvp与噪声右侧函数信息。为了克服右侧有噪声函数的挑战，使用了正则化的思想。数值模拟表明了该方法的优越性。

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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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.