A modified linear approximation for weakly singular integrals

• Autorzy: Nadir M.
• Języki publikacji: EN

Abstrakty

EN

In this work, we present a new approximation for a weakly singular integral, in particular Abel's integral. This approximation is based on the modification of the linear spline function, this one leads to eliminate the weak singularity. Noting that, it is clear that in the future we use this approximation for solving numerically all weakly singular integrals equations on an oriented smooth curve or on an interval.

Słowa kluczowe

EN

Abel’s integral; weakly singular integral; interpolation

• Wydawca: Komisja Informatyki Polskiej Akademii Nauk, Oddział w Gdańsku
• Czasopismo: Journal of Theoretical and Applied Computer Science
• Rocznik: 2015
• Tom: Vol. 9, nr 4
• Strony: 19--25
• Opis fizyczny: Bibliogr. 7 poz., tab., wz.

Twórcy

autor

Nadir M.

• Department of Mathematics, University of Msila, Algeria

Bibliografia

• [1] J. Abdekhani, A numerical approach to the Abel integral equations of the second kind with non smooth solution, in Journal of Computational and Applied Mathematics 29 (1990) 249-255.
• [2] K. Maleknejad, M. Nosrati, E. Najafi, Wavelet Galerkin method for solving singular integraf equations, in Computational and Applied Mathematics 31,(2) (2012) 373–390.
• [3] M. Nadir, Adapted Quadratic Approximation for Singular Integrals, in Journal of mathematical Inequalities 4, (3) pp 423-430 (2010)
• [4] M. Nadir, Adapted Linear Approximation for Singular Integrals, in Mathematical sciences 6, (36) (2012).
• [5] M. Nadir, Adapted Quadratic Approximation for Logarithmic Kernel Integrals, in Fasciculi Mathematici 49, (2) pp 75-85 (2012).
• [6] M. Nadir, B. Lakehali, Adapted Quadratic Approximation For Weakly Singular Integrals, in Applied Mathematics E-Notes. 15 (2015), 225-232.
• [7] A. Shahsavaran, Numerical Approach to Solve Second Kind Volterra Integral Equation of Abel Type Using Block-Pulse Functions and Taylor Expansion by Collocation Method, in Applied Mathematical Sciences, 5,(14) 2011, 685 - 696.