求解四阶积分微分方程的高阶哈小波方法

IF 3.1 3区计算机科学 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Science Pub Date : 2024-07-25 DOI:10.1016/j.jocs.2024.102394

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引用次数: 0

摘要

本文提出了一种求解三阶和四阶积分微分方程（IDE）的数值方法。为了确定二阶三阶和四阶积分微分方程的数值解法，采用了新引入的高阶哈小波方法（HOHWM），与经典哈小波方法相比，提高了数值结果和收敛速度。为了验证 HOHWM 的有效性，我们解决了文献中的一些实例。为确保所提出的方法合法、适用并实现其目标，计算了每个测试问题在测试点的最大绝对误差。

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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Higher-order Haar wavelet method for solution of fourth-order integro-differential equations

This paper presents a numerical approach to solve third and fourth order intego-differential equations (IDEs). In order to ascertain the numerical solution for third and fourth order IDEs of second kind, the newly introduced Higher order Haar wavelet method (HOHWM) has been employed to improve the numerical result and rate of convergence compared to classical Haar wavelet approach. Some examples available in the literature have been solved to verify the HOHWM’s effectiveness. To ensure that the approach presented is legitimate, applicable and achieves its objective, the maximum absolute error of each test problem is calculated at a test point.

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来源期刊

Journal of Computational Science COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS-COMPUTER SCIENCE, THEORY & METHODS

CiteScore

5.50

自引率

3.00%

发文量

227

审稿时长

41 days

期刊介绍： Computational Science is a rapidly growing multi- and interdisciplinary field that uses advanced computing and data analysis to understand and solve complex problems. It has reached a level of predictive capability that now firmly complements the traditional pillars of experimentation and theory. The recent advances in experimental techniques such as detectors, on-line sensor networks and high-resolution imaging techniques, have opened up new windows into physical and biological processes at many levels of detail. The resulting data explosion allows for detailed data driven modeling and simulation. This new discipline in science combines computational thinking, modern computational methods, devices and collateral technologies to address problems far beyond the scope of traditional numerical methods. Computational science typically unifies three distinct elements: • Modeling, Algorithms and Simulations (e.g. numerical and non-numerical, discrete and continuous); • Software developed to solve science (e.g., biological, physical, and social), engineering, medicine, and humanities problems; • Computer and information science that develops and optimizes the advanced system hardware, software, networking, and data management components (e.g. problem solving environments).