Integral equations with Cauchy kernel in the contact problem

Journal of Applied Mathematics and Computing

Volumn 7, Issue 3, 2000, Pages 663-672

  Abdou, M A ^a  

^a Alexandria University   (Egypt)

Author keywords

Cauchy kernel; Hertz problem; Integral equation; Jacobi polynomial; Orthogonal polynomials

Indexed keywords

NUMERICAL METHODS; POLYNOMIALS;

ARBITRARY SHAPE; CAUCHY KERNELS; CONTACT PROBLEM; HERTZ PROBLEM; JACOBI POLYNOMIALS; ORTHOGONAL POLYNOMIAL; POTENTIAL FUNCTION; SECOND KINDS;

INTEGRAL EQUATIONS;

EID: 0041868800     PISSN: 15985865     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf03012276     Document Type: Article

References (18)

1. A. Gerasoulis, The use of piecewise quadratic polynomials for the solution of singular integral equations of Cauchy type, Comp. and Math. with Appl. 8, (1982), pp. 15-22.
2. C. D. Green, Integral equation Methods, Nelson, New York, 1969.
3. E. Venturino, The Galerkin method for singular integral equations resisted, J. Comp. Appl. Math. 40, (1992), pp. 91-103.
4. F. G. Tricomi, Integral equations, Dover, New York, 1985.
5. G. R. Miller and L. M. Keer, A numerical technique for the solution of singular integral equations of the second kind, Quart. Appl. Math., January (1985), pp. 455-466.
6. G. Ya. Popov, Contact problems for a linearly de formable base, Kiev, Odessa, 1982.
7. I. C. Gradchtein and I. M. Reguk, Tables of integrals, sums and products, Nauka, Moscow, 1962.
8. J. Frankel, A Galerkin solution to a regularized Cauchy singular integro-differential equation, Quart. Appl. Math. Vol. Lib. No. 2, (1995), pp. 245-258.
9. J. R. Willis and S. Nemat-Nasser, Singular perturbation solution of a class of singular integral equations, Quart. Appl. Math., XLVIII, No. 4, (1990), pp. 741-753.
10. K. E. Atkinson, A survey of numerical methods for the solution of Fredholm integral equation of the second kind, SIAM. Philadelphia, 1976.
11. L. M. Delves and J. L. Mohamed, Computational methods for integral equations, Philadelphia, New York, 1985.
12. M. A. Abdou and S. A. Hassam, Boundary value of a contact problem, PU, M. A., Vol. 5, No. 3, (1994), pp. 311-316.
13. M. A. Abdou and N. Y. Ezz-Eldin, Krein's method with certain singular kernel for solving the integral equation of the first kind, Periodica Math. Hung. Vol. 28, (1994), pp. 143-149.
14. M. A. Golberg, The convergence of a collocation method for a class of a Cauchy singular integral equations, J. Math. Anal. Appl. 100, (1984), pp. 500-512.
15. N. I. Muskhelishvili, Singular integral equations, Noordroof, Groningen, 1953.
16. N. I.Muskhelishvili, Some basic problems of mathematical theory of elasticity,Moscow, 1949.
17. P. Linz, Analytical and numerical methods for Volterra equations, SIAM, Philadelphia, 1985.
18. V. M. Aleksandrov and E. V. Kovalenko, Problems with mixed boundary conditions in continuous mechanics, Nauka, Moscow, 1986.