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 $\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. 
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     author = {Maria Capcelea and Titu Capcelea},
     title = {B-spline collocation method for solving {Fredholm} integral equations with discontinuous right-hand side},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {92--101},
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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. http://geodesic.mathdoc.fr/item/BASM_2023_2_a7/