On the numerical treatment of the singular integral equation of the second kind

Applied Mathematics and Computation

Volumn 146, Issue 2-3, 2003, Pages 373-380

  Abdou, M A ^a   Nasr, A A ^b  

^a Alexandria University   (Egypt)

^b NONE

Author keywords

A system of linear algebraic equation; Cauchy kernel; Legendre polynomial; Singular integral equation

Indexed keywords

APPROXIMATION THEORY; LINEAR EQUATIONS; POLYNOMIALS; PROBLEM SOLVING;

CAUCHY KERNEL;

INTEGRAL EQUATIONS;

EID: 0041689399     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(02)00587-8     Document Type: Article

References (18)

1. Gerasoulis A. The use of piecewise quadratic polynomial for the solution of singular integral equation of Cauchy type. Comp. Math. Appl. 8:1982;15-22.
2. Green C.D. Integral Equation Method. 1969;Nelson, New York.
3. Venturino E. The Glerkin method for singular integral equations revisited. J. Comp. Appl. Math. 40:1992;91-103.
4. Tricomi F.G. Integral Equations. 1985;Dover, New York.
5. Miller G.R., Keer L.M. A numerical technique for the solution of singular integral equations of the second kind. Quart. Appl. Math. 1985;455-466.
6. Popov G.Ya. Contact Problem for a Linearly Deformable Base. 1982;Kiev, Odessa.
7. Gradchtein L.C., Rezuk I.M. Tables of Integrals, Sums, Products. 1962;Nauka, Moscow.
8. Frankel J. A Galerkin solution to a regularized Cauchy singular integro-differential equation. Quart. Appl. Math. Vol. Lib. 2:1988;245-258.
9. Willis J.R., Nemat-Nasser S. Singular pertulation solution of a class of singular integral equations. Quart. Appl. Math. XLV111(4):1990;741-753.
10. Atkinson K.E. A Survey of Numerical Methods for the Solution of Fredholm Integral Equations of the Second Kind. 1976;SIAM, Philadelphia, PA.
11. L.M. Deleves, J.L. Mohamed, Computational Methods for Integral Equations, New York, 1985.
12. M.A. Abdou, S.A. Hassan, Boundry value of a contact problem, PU, MA, 5 (3) (1994) 311-316.
13. Abdou M.A., Ezz-Eldin N.Y. Krein's method with certain singular kernel for solving the integral equation of the first kind. Periodica Math. Hung. 28(2):1994;143-149.
14. Golberg M.A. The convergence of a collocation method for a class of a Cauchy singular integral equations. J. Math. Anol. Appl. 100:1984;500-512.
15. Muskhelishvili N.I. Singular Integral Equations. 1953;Noordhoff, Groningen.
16. N.I. Muskhelishvili, Some Problems of Mathematical Theory of Elasticity, Moscow, 1949.
17. Linz P. Analytical and numerical methods for Voltera equations. 1985;SIAM, Philadelphia, PA.
18. Alexandrov V.M., Kovalenko E.V. Problems with Mixed Boundary Conditions in Continuum Mechanics. 1986;Nauka, Moscow.