Exploring error estimates of Newton-Cotes quadrature rules across diverse function classes
Abstract This in-depth study looks at symmetric four-point Newton-Cotes-type inequalities with a focus on error estimates for numerical integration. The precision of these estimates is explored across various classes of functions, including those with bounded variation, bounded derivatives, Lipschit...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-01-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | https://doi.org/10.1186/s13660-025-03251-4 |
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| _version_ | 1832594342356713472 |
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| author | Abdelghani Lakhdari Muhammad Uzair Awan Silvestru Sever Dragomir Hüseyin Budak Badreddine Meftah |
| author_facet | Abdelghani Lakhdari Muhammad Uzair Awan Silvestru Sever Dragomir Hüseyin Budak Badreddine Meftah |
| author_sort | Abdelghani Lakhdari |
| collection | DOAJ |
| description | Abstract This in-depth study looks at symmetric four-point Newton-Cotes-type inequalities with a focus on error estimates for numerical integration. The precision of these estimates is explored across various classes of functions, including those with bounded variation, bounded derivatives, Lipschitzian derivatives, convex derivatives, and others. The research synthesizes and extends existing knowledge, providing a nuanced understanding of how error bounds depend on the characteristics of integrated functions. Through a systematic review of seminal works, the study contributes to the practical application of numerical integration techniques, offering insight for researchers and practitioners to make informed choices based on the specific features of the functions involved. |
| format | Article |
| id | doaj-art-6e8179a922a54fd68b2a3cff7cb4f428 |
| institution | Kabale University |
| issn | 1029-242X |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj-art-6e8179a922a54fd68b2a3cff7cb4f4282025-01-19T12:43:00ZengSpringerOpenJournal of Inequalities and Applications1029-242X2025-01-012025112310.1186/s13660-025-03251-4Exploring error estimates of Newton-Cotes quadrature rules across diverse function classesAbdelghani Lakhdari0Muhammad Uzair Awan1Silvestru Sever Dragomir2Hüseyin Budak3Badreddine Meftah4Department CPST, National Higher School of Technology and EngineeringDepartment of Mathematics, Government College UniversityApplied Mathematics Research Group, ISILC, Victoria UniversityDepartment of Mathematics, Faculty of Science and Arts, Düzce UniversityLaboratory of Analysis and Control of Differential Equations “ACED”, Facuty MISM, Department of Mathematics, University of 8 May 1945 GuelmaAbstract This in-depth study looks at symmetric four-point Newton-Cotes-type inequalities with a focus on error estimates for numerical integration. The precision of these estimates is explored across various classes of functions, including those with bounded variation, bounded derivatives, Lipschitzian derivatives, convex derivatives, and others. The research synthesizes and extends existing knowledge, providing a nuanced understanding of how error bounds depend on the characteristics of integrated functions. Through a systematic review of seminal works, the study contributes to the practical application of numerical integration techniques, offering insight for researchers and practitioners to make informed choices based on the specific features of the functions involved.https://doi.org/10.1186/s13660-025-03251-4Newton-Cotes inequalitiesFunctions of bounded variationLipschitzian functionsBounded functionsConvex functions |
| spellingShingle | Abdelghani Lakhdari Muhammad Uzair Awan Silvestru Sever Dragomir Hüseyin Budak Badreddine Meftah Exploring error estimates of Newton-Cotes quadrature rules across diverse function classes Journal of Inequalities and Applications Newton-Cotes inequalities Functions of bounded variation Lipschitzian functions Bounded functions Convex functions |
| title | Exploring error estimates of Newton-Cotes quadrature rules across diverse function classes |
| title_full | Exploring error estimates of Newton-Cotes quadrature rules across diverse function classes |
| title_fullStr | Exploring error estimates of Newton-Cotes quadrature rules across diverse function classes |
| title_full_unstemmed | Exploring error estimates of Newton-Cotes quadrature rules across diverse function classes |
| title_short | Exploring error estimates of Newton-Cotes quadrature rules across diverse function classes |
| title_sort | exploring error estimates of newton cotes quadrature rules across diverse function classes |
| topic | Newton-Cotes inequalities Functions of bounded variation Lipschitzian functions Bounded functions Convex functions |
| url | https://doi.org/10.1186/s13660-025-03251-4 |
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