2. Articole
Permanent URI for this collectionhttps://msuir.usm.md/handle/123456789/17
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Item A NUMERICAL METHOD FOR SOLVING SINGULAR INTEGRAL EQUATIONS WITH PIECEWISE CONTINUOUS COEFFICIENTS(CEP USM, 2024) Capcelea, Maria; Capcelea, TituThe 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.Item B-SPLINE APPROXIMATION OF DISCONTINUOUS FUNCTIONS DEFINED ON A CLOSED CONTOUR IN THE COMPLEX PLANE(2022) Capcelea, Maria; Capcelea, TituIn this paper we propose an efficient algorithm for approximating piecewise continuous functions, defined on a closed contour Γ in the complex plane. The function, defined numerically on a finite set of points of Γ, is approximated by a linear combination of B-spline functions and Heaviside step functions, defined on Γ. Theoretical and practical aspects of the convergence of the algorithm are presented, including the vicinity of the discontinuity points.Item LOCALIZATION OF SINGULAR POINTS OF MEROMORPHIC FUNCTIONS BASED ON INTERPOLATION BY RATIONAL FUNCTIONS(2021) Capcelea, Maria; Capcelea, TituIn this paper we examine two algorithms for localization of singular points of meromorphic functions. Both algorithms apply approximation by interpolation with rational functions. The first one is based on global interpolation and gives the possibility to determine the singular points of the function on a domain that includes a simple closed contour on which the values of the function are known. The second algorithm, based on piecewise interpolation, establishes the poles and the discontinuity points on the contour where the function values are given.Item LAURENT-PAD ́E APPROXIMATION FOR LOCATING SINGULARITIES OF MEROMORPHIC FUNCTIONS WITH VALUES GIVEN ON SIMPLE CLOSED CONTOURS(Institutul de Matematică şi Informatică al AŞM, 2020) Capcelea, Maria; Capcelea, TituIn the present paper the Pad ́e approximation with Laurent polynomials is examined for a meromorphic function on a finite domain of the c omplex plane. Values of the function are given at the points of a simple closed cont our from this domain. Based on this approximation, an efficient numerical algorith m for locating singular points of the function is proposed.