A numerical solution to the system of Cauchy singular integral equations with unbounded endpoint conditions

B. Sahu, A. Setia, M.T. Nair and A. Yadav

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 248, issue C, 26-41

Abstract: We propose a residual-based Galerkin’s approach to solve a system of Cauchy-type singular integral equations with unbounded endpoint conditions. The Chebyshev polynomials of the first kind are used to approximate the solution. A comprehensive analysis is conducted to establish the well-posedness of the system and the given numerical scheme. We derive theoretical error bounds and validate them through numerical examples. Numerical implementation via two crack problems has also been shown, where the strain is estimated by Chebyshev polynomials of the first kind. Stress intensity factors near the tips of the cracks have also been computed.

Keywords: Chebyshev polynomial; Cauchy singular integral equation; Error bound; Stress intensity factor; Crack problem (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:248:y:2026:i:c:p:26-41

DOI: 10.1016/j.matcom.2026.04.002

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