B-spline collocation method for solving Fredholm integral equations with discontinuous right-hand side
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Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis (246)
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CAPCELEA, Maria, CAPCELEA, Titu. B-spline collocation method for solving Fredholm integral equations with discontinuous right-hand side. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2023, nr. 2(102), pp. 92-101. ISSN 1024-7696. DOI: https://doi.org/10.56415/basm.y2023.i2.p92
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
Numărul 2(102) / 2023 / ISSN 1024-7696 /ISSNe 2587-4322

B-spline collocation method for solving Fredholm integral equations with discontinuous right-hand side

DOI:https://doi.org/10.56415/basm.y2023.i2.p92
CZU: 517.968

Pag. 92-101

Capcelea Maria, Capcelea Titu
 
Moldova State University
 
 
 
Disponibil în IBN: 29 noiembrie 2023


Rezumat

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

Cuvinte-cheie
Fredholm integral equation, piecewise continuous function, closed contour, complex plane, Numerical approximation, B-spline, step function, convergence