A quadrature method for Volterra integral equations of the first kind

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 15 شهریور 1404

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2025.95004.1712

نویسنده

Seyyed Ahmad Hosseini^*

Department of Mathematics, Faculty of Sciences, Golestan University, Gorgan, Iran.

چکیده

This paper introduces a direct quadrature method for the numerical solution of Volterra integral equations of the first kind, utilizing a composite quadrature scheme based on the Floater--Hormann family of linear barycentric rational interpolants. The convergence of the proposed method is rigorously proved, and the order of convergence is explicitly derived in terms of the parameters of the method, thereby providing a clear theoretical framework for its performance. Several numerical experiments are provided to demonstrate both the efficiency and accuracy of the method, as well as to verify the excellent agreement between the implementation results and the theoretically predicted convergence rates.

کلیدواژه‌ها

Volterra integral equations؛ Direct quadrature method؛ Rational interpolation؛ Barycentric form