Abstract:
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.
Keywords and phrases:fredholm integral equation, piecewise continuous function, closed contour, complex plane, numerical approximation, B-spline, step function, convergence.
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