An Approach to Volterra and Fredholm IntegroDifferential Equations via Six Non-Polynomial Cubic Spline functions.
This study introduces an effective numerical method for approximating solutions to Volterra and Fredholm integrodifferential equations through a novel general formulation of non-polynomial cubic spline functions (NCSF). The proposed method enhances spline techniques by integrating trigonometric and...
| Publicado en: | Journal of Basrah Researches (Sciences) Vol. 52; no. 1; pp. 32 - 51 |
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| Autores principales: | , , |
| Formato: | Artículo |
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Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR)
2026
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| Materias: | |
| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=195078479&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 195078479 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 18172695 GYGY jtl: Journal of Basrah Researches (Sciences) issn: 18172695 maglogo: N pubinfo: dt: 2026 vid: 52 iid: 1 pid: 25427 pub: Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) artinfo: ui: 195078479 10.56714/bjrs.52.1.3 ppf: 32 ppct: 19 formats: tig: atl: An Approach to Volterra and Fredholm IntegroDifferential Equations via Six Non-Polynomial Cubic Spline functions. aug: au: Qadir, Rahel J. Mohammedfaeq, Shabaz Jalil Hamasalh, Faraidun K. affil: Department of Mathematical Science, College of Basic Education, University of Sulaimani, Sulaymaniyah 46001, Iraq. Department of Mathematics, College of Science, University of Sulaimani, Sulaymaniyah 46001, Iraq. Department of Mathematics, College of Education, University of Sulaimani, Sulaymaniyah 46001, Iraq. su: Volterra equations Fredholm equations Numerical analysis Spline theory Python programming language sug: subj: Volterra equations Fredholm equations Numerical analysis Spline theory Python programming language keyword: Collocation Method Convergence Analysis Integro-Differential Equations Non-Polynomial Cubic Splines Numerical Approximation التقریب العددي المعادلات التكاملیة التفاضلیة المنحنیات المكعبة غیر متعددة تحلیل التقارب طریقة التجمیع ab: This study introduces an effective numerical method for approximating solutions to Volterra and Fredholm integrodifferential equations through a novel general formulation of non-polynomial cubic spline functions (NCSF). The proposed method enhances spline techniques by integrating trigonometric and exponential components with six non-polynomial cubic spline function formulations. A comprehensive convergence analysis occurs, establishing sufficient conditions for the stability and error bounds of the method. Multiple test problems are addressed, including Volterra and Fredholm integrodifferential equations. The resulting numerical outcomes are compared with exact solutions and methodologies from the literature, presented in tables and figures. Comparisons illustrate the efficacy and robustness of the proposed six non-polynomial cubic spline method in addressing Volterra and Fredholm problems while obtaining higher precision with fewer grid points, as demonstrated by computational reports generated using Python 3.12.4. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y dt: @attributes: year: 2026 holdings: @attributes: islocal: N |
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