Geodesic
B-spline collocation method for solving Fredholm integral equations with discontinuous right-hand side
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2023), pp. 92-101.

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In this paper, we propose a method for approximating the solution of the linear Fredholm integral equation of the second kind which is defined on a closed contour Γ in the complex plane. The right-hand side of the equation is a piecewise continuous function that is numerically defined on a finite set of points on Γ. To approximate the solution, we use a linear combination of B-spline functions and Heaviside step functions defined on Γ. We discuss both theoretical and practical aspects of the pointwise convergence of the method, including its performance in the vicinity of the points where discontinuities occur. 
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Maria Capcelea; Titu Capcelea. B-spline collocation method for solving Fredholm integral equations with discontinuous right-hand side. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2023), pp. 92-101. https://geodesic-test.mathdoc.fr/item/BASM_2023_2_a7/

[1] T. Capcelea, “Collocation and quadrature methods for solving singular integral equations with piecewise continuous coefficients”, Buletinul Academiei de Stiinte a Republicii Moldova. Matematica, 2006, no. 3(52), 27–44 | MR | Zbl

[2] M. Capcelea, T. Capcelea, “Algorithms for efficient and accurate approximation of piecewise continuous functions”, Abstracts of the conference “Mathematics Information Technologies: Research and Education (MITRE-2016)” (Chisinau, June 23-26, 2016), 15

[3] M. Capcelea, T. Capcelea, “B-spline approximation of discontinuous functions defined on a closed contour in the complex plane”, Buletinul Academiei de Stiinte a Republicii Moldova. Matematica, 2022, no. 2(99), 59–67 | MR

[4] M. Capcelea, T. Capcelea, Approximation of piecewise continuous functions, CEP USM, Chişinău, 2022, 110 pp. (in Romanian)

[5] M. Capcelea, T. Capcelea, “Laurent-Padé approximation for locating singularities of meromorphic functions with values given on simple closed contours”, Buletinul Academiei de Stiinte a Republicii Moldova. Matematica, 2020, no. 2(93), 76–87 | MR | Zbl

[6] M. Capcelea, T. Capcelea, “Localization of singular points of meromorphic functions based on interpolation by rational functions”, Buletinul Academiei de Stiinte a Republicii Moldova. Matematica, 2021, no. 1–2(95–96), 110–120 | MR | Zbl

[7] L.N. Trefethen, J. Weideman, “The exponentially convergent trapezoidal rule”, SIAM Review, 56:3 (2014), 385–458 | DOI | MR | Zbl