{"title":"Higher-order Haar wavelet method for solution of fourth-order integro-differential equations","authors":"","doi":"10.1016/j.jocs.2024.102394","DOIUrl":null,"url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":48907,"journal":{"name":"Journal of Computational Science","volume":null,"pages":null},"PeriodicalIF":3.1000,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational Science","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S187775032400187X","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
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Abstract
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.
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).
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