{"title":"Numerical integration of third-order BVPs using a fourth-order hybrid block method","authors":"Mufutau Ajani Rufai","doi":"10.1016/j.jocs.2024.102338","DOIUrl":null,"url":null,"abstract":"<div><p>This research paper introduces a new hybrid block method to solve the third-order boundary value problems (BVPs). The method combines interpolation and collocation and uses a power series polynomial to find an approximate solution to the considered third-order BVPs. Some third-order BVP models are numerically solved to verify the performance and efficiency of the proposed method, and the approximate solution from the proposed method is more efficient when compared to some existing numerical methods. In summary, the proposed method provides reliable and efficient accuracy for solving third-order BVPs, making it a valuable contribution to the fields of numerical analysis and computational mathematics. The advantages of the proposed method include improved computational time efficiency and accuracy in terms of maximum absolute errors for solving third-order BVPs.</p></div>","PeriodicalId":48907,"journal":{"name":"Journal of Computational Science","volume":null,"pages":null},"PeriodicalIF":3.1000,"publicationDate":"2024-05-23","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/S1877750324001315","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}
引用次数: 0
Abstract
This research paper introduces a new hybrid block method to solve the third-order boundary value problems (BVPs). The method combines interpolation and collocation and uses a power series polynomial to find an approximate solution to the considered third-order BVPs. Some third-order BVP models are numerically solved to verify the performance and efficiency of the proposed method, and the approximate solution from the proposed method is more efficient when compared to some existing numerical methods. In summary, the proposed method provides reliable and efficient accuracy for solving third-order BVPs, making it a valuable contribution to the fields of numerical analysis and computational mathematics. The advantages of the proposed method include improved computational time efficiency and accuracy in terms of maximum absolute errors for solving third-order BVPs.
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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