A NUMERICAL METHOD FOR SOLVING SINGULAR INTEGRAL EQUATIONS WITH PIECEWISE CONTINUOUS COEFFICIENTS
Date
2024
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
CEP USM
Abstract
The present study is dedicated to developing an efficient computational scheme for solving the Cauchy singular integral equation, defined on a closed and smooth contour in the complex plane. The coefficients and the right-hand side of the equation are piecewise continuous functions, numerically defined on a finite set of points along the contour. The approximate solution is constructed as a linear combination of B-spline functions and Heaviside functions, with coefficients determined using the collocation method. This method generates a sequence of approximations that converge almost uniformly to the exact solution of the equation.
Description
Keywords
singular integral equation, piecewise continuous coefficients, computational scheme, B-spline functions
Citation
CAPCELEA, Maria and Titu CAPCELEA. Numerical method for solving singular integral equations with piecewise continuous coefficients. In: Integrare prin cercetare și inovare: conferință științifică națională cu participare internațională. Științe exacte și ale naturii, Chișinău, 7-8 noiembrie, 2024. Chișinău: CEP USM, 2024, pp. 726-733. ISBN 978-9975-62-808-2 (PDF). Disponibil: https://doi.org/10.59295/spd2024n.100