Cubic spline quasi-interpolation operator to numerically solve integro-differential equations with weakly singular kernels

C. Allouch, D. Barrera, A. Saou and M. Tahrichi

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 230, issue C, 413-422

Abstract: In this paper we use cubic spline quasi-interpolant operator to numerically address a class of linear integro-differential equations with weakly singular kernel. As stated in Pedas and Tamme (2006), the exact solution of this equation lacks the desired level of smoothness and belongs to a particular function space. Then, in the first part of this paper, we analyze the approximation properties of the cubic spline quasi-interpolant operator in this particular space. Subsequently, we use these results in the analysis of the quasi-collocation method used to solve an integro-differential equation with weakly singular kernel. Also, some numerical tests are provided to confirm the theoretical results.

Keywords: Quasi-interpolants operators; Fredholm integro-differential equations; Weakly singular kernel; Graded grids (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:230:y:2025:i:c:p:413-422

DOI: 10.1016/j.matcom.2024.03.014

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