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 
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. http://geodesic.mathdoc.fr/item/BASM_2023_2_a7/
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     title = {B-spline collocation method for solving {Fredholm} integral equations with discontinuous right-hand side},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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 $\Gamma $ 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 $\Gamma $. To approximate the solution, we use a linear combination of B-spline functions and Heaviside step functions defined on $\Gamma $. 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.

[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