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...

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Publicado en:Journal of Basrah Researches (Sciences) Vol. 52; no. 1; pp. 32 - 51
Autores principales: Qadir, Rahel J., Mohammedfaeq, Shabaz Jalil, Hamasalh, Faraidun K.
Formato: Artículo
Publicado: Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) 2026
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Acceso en línea:Ver este registro en EBSCOhost
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        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
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