Approximation solution for singular integral equations with logarithmic kernel using adapted linear spline

• Autorzy: Nadir M.
• Języki publikacji: EN

Abstrakty

EN

In this work, we apply a direct method for an approximative solution of a weakly singular integral equations (W.S.I.E) with logarithmic kernel on an oriented smooth contour using a modified linear spline approximation, we also show that this approximation gives an efficient approach to the analytical solution of (W.S.I.E)

Słowa kluczowe

EN

weakly singular integral; spline function; Hőlder space; Hőlder condition

• Wydawca: Komisja Informatyki Polskiej Akademii Nauk, Oddział w Gdańsku
• Czasopismo: Journal of Theoretical and Applied Computer Science
• Rocznik: 2016
• Tom: Vol. 10, nr 1
• Strony: 19--25
• Opis fizyczny: Bibliogr. 9 poz., rys., tab.

Twórcy

autor

Nadir M.

• Department of Mathematics, University of Msila, Algeria

Bibliografia

• [1] Antidze, D. J.: On the approximate solution of singular integral equations, Seminar of Institute of Applied Mathematics, 1975, Tbilissi.
• [2] Muskhelishvili, N. I.: Singular integral equations, Nauka, Moscow, 1968, English transl, of 1sted Noordhoff, 1953; reprint, 1972.
• [3] Nadir, M., Antidze, J.: On the numerical solution of singular integral equations using Sanikidze’s approximation, Comp Math in Sc. Tech. 10(1) (2004), 83-89.
• [4] Nadir, M., Lakehali, B.: On The Approximation of Singular Integrals FEN DERGĺSĺ (E-DERGĺ), 2(2)(2007), 236-2400
• [5] Nadir, M.: Adapted Linear Approximation for Singular Integrals, in Mathematical sciences 6, (36) 2012.
• [6] Nadir, M.: Adapted linear Approximation for Logarithmic kernel Integrals, in Journal of Approximation Theory and Applied Mathematics 3 (2014), 37-44.
• [7] Prossdorf, S., Saranen, J., Sloan, I. H.: A discrete method for the logarithmic kernel integral equation on an open arc, in 3. Austral. Math. Soc. Ser. B 34(1993), 401-418
• [8] Sanikidze, J.: Approximate solution of singular integral equations in the case of closed contours of integration, Seminar of Institute of Applied Mathematics, 1971, Tbilissi
• [9] Saranen, J.: The modified quadrature method for logarithmic-kernel integral equations on closed curves, in J. Integral Equations Appl. 3(4) (1991), 575-600.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).