A high-order Haar wavelet approach to solve differential equations of fifth-order with simple, two-point and two-point integral conditions

IF 2.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2025-09-10 DOI:10.1016/j.apnum.2025.09.004

Maher Alwuthaynani , Muhammad Ahsan , Weidong Lei , Muhammad Abuzar , Masood Ahmad , Aditya Sharma

引用次数: 0

Abstract

This study introduces a high-order Haar wavelet collocation method (HHWCM) as an enhanced version of the classical Haar wavelet collocation method (HWCM) for solving fifth-order ordinary differential equations (FoDEs) subject to simple, two-point, and integral boundary conditions. By incorporating a quasi-linearization strategy, the proposed method avoids Jacobian computations and achieves higher accuracy with faster convergence. The stability and convergence of the approach are rigorously analyzed. Numerical experiments on both linear and nonlinear FoDEs demonstrate that HHWCM significantly outperforms HWCM and other existing numerical methods in terms of precision, computational efficiency, and robustness across diverse problem settings.

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用高阶Haar小波方法求解五阶微分方程的简单、两点和两点积分条件

本文引入了一种高阶Haar小波配置方法（HHWCM），作为经典Haar小波配置方法（HWCM）的改进版本，用于求解具有简单、两点和积分边界条件的五阶常微分方程（FoDEs）。该方法采用准线性化策略，避免了雅可比矩阵的计算，收敛速度快，精度高。严格分析了该方法的稳定性和收敛性。在线性和非线性FoDEs上进行的数值实验表明，HHWCM在精度、计算效率和鲁棒性方面明显优于HWCM和其他现有的数值方法。

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.