Metoda B-spline colocaţiei pentru ecuaţii integrale Fredholm cu membrul drept discontinuu [Articol]

Abstract

In this paper, we propose a numerical method for approximating solutions to linear Fredholm integral equations of the second kind, defined on a closed contour in the complex plane. The right-hand side is a piecewise continuous function given numerically at a finite set of points on the contour. The approximation is constructed using a linear combination of B-spline functions and Heaviside step functions defined on the same domain. We analyze both the theoretical and practical aspects of the method’s pointwise convergence, with particular attention to its behavior near discontinuity points.