Acceleration of convergence in approximate solutions of Urysohn integral equations with Green’s kernels

Shashank K. Shukla and Gobinda Rakshit

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 240, issue C, 681-697

Abstract: Consider a non-linear operator equation x−K(x)=f, where f is a given function and K is a Urysohn integral operator with Green’s function type kernel defined on L∞[0,1]. We apply approximation methods based on interpolatory projections onto the approximating space Xn, which is the space of piecewise polynomials of even degree with respect to a uniform partition of [0,1]. The approximate solutions obtained from these methods demonstrate enhanced accuracy compared to the classical collocation solution for the same equation. Numerical examples are given to support our theoretical results.

Keywords: Urysohn integral operator; Green’s kernel; Interpolatory operator; Collocation points (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:240:y:2026:i:c:p:681-697

DOI: 10.1016/j.matcom.2025.07.044

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