On the solution of linear and nonlinear integral equation

Applied Mathematics and Computation

Volumn 146, Issue 2-3, 2003, Pages 857-871

  Abdou, M A ^a  

^a Alexandria University   (Egypt)

Author keywords

F VIE; Fredholm Volterra integral equation; Linear integral equation; Logarithmic kernel; Nonlinear integral equation; Potential function

Indexed keywords

BESSEL FUNCTIONS; BOUNDARY VALUE PROBLEMS; CHEBYSHEV APPROXIMATION; LINEAR EQUATIONS; NONLINEAR EQUATIONS; POLYNOMIALS; PROBLEM SOLVING;

POTENTIAL FUNCTIONS;

INTEGRAL EQUATIONS;

EID: 0041736687     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(02)00643-4     Document Type: Article

References (44)

1. Constanda C. Integral equation of the first kind in plane elasticity. J. Quart. Appl. Math. LIII(4):1995;783-793.
2. Gori L., Santi E., Cimoroni M.G. Projector-splines in the numerical solution of integro-differential equations. Comput. Math. Appl. 35(5):1998;107-116.
3. Brunner H., Makroglou A., Miller R.K. On mixed collocation method for Volterra integral equations with periodic solution. Appl. Numer. Math. 24:1997;115-130.
4. Muskhelishvili N.I. Singular Integral Equations. 1953;Noordhoff, Leiden.
5. C.D. Green, Integral Equation Methods, Nelson, NY, 1969.
6. A. Dzhuraev, Methods of Singular Integral Equations, London, NY, 1992.
7. R.P. Kanwal, Linear Integral Equations Theory and Technique, Boston, 1996.
8. K.E. Atkinson, A Survey of Numerical Method for the Solution of Fredholm Integral Equation of the Second Kind, Philadelphia, 1976.
9. K.E. Atkinson, The Numerical Solution of Integral Equation of the Second Kind, Cambridge, 1997.
10. L.M. Delves, J.L. Mohamed, Computational Methods for Integral Equations, London, NY, 1985.
11. Baker C.T.H. Treatment of Integral Equations by Numerical Methods. 1982;Academic press.
12. M.A. Golberg, Numerical Solution of Integral Equations, New York, 1990.
13. Abdou M.A., Hassan S.A. Fredholm integral equation with singular kernel. Korean J. Comput. Appl. Math. 7(1):2000;223-236.
14. Abdou M.A. Integral equations with Cauchy kernel in the contact problem. Korean J. Comput. Appl. Math. 7(3):2000;663-672.
15. Abdou M.A. On asymptotic method in contact problems of Fredholm integral equation of the second kind. Korean J. Comput. Appl. Math. 9:2002;261-275.
16. M.A. Abdou, M. Basseem, A numerical method for solving Fredholm integral equation of the second kind with Cauchy kernel, Canadian J. Phys., in press.
17. Abdou M.A. Fredholm-Volterra integral equation of the first kind and contact problem. Appl. Math. Comput. 125:2002;177-193.
18. M.H. Fahmy, M.A. Abdou, E.I. Deebs, Fredholm-Volterra integral equation of the first kind with potential kernel, Le Mathematiche, vol. LV (200)-Fasc. (1), pp. 55-74.
19. Abdou M.A. Integral equation of mixed type and integrals of orthogonal polynomials. J. Comp. Appl. Math. 138:2002;273-285.
20. G.Ya. Popov, Contact Problems for a Linearly Deformable Base, Kiev, Odessa, 1982.
21. Linz P. Analytic and Numerical Methods for Volterra Equations. 1985;SIAM, Philadelphia.
22. T.A. Burton, Volterra Integral and Differential Equations, London, NY, 1983.
23. Bannas J. Integrable solution of Hammerstein and Urysohn integral equations. J. Aust. Math. Soc. A. 46:1989;61-68.
24. Emmanuele G. Integrable solutions of functional integral equations. J. Integral Equat. Appl. 4:1992;89-94.
25. Emmanuele G. Integrable solutions of Hammerstein equations. Appl. Anal. 50:1993;277-284.
26. Hocia L. Approximate solutions of the system of Hammerstein integral equations. Fasciculi Mathematici. 18:1988.
27. Hacia L. Solving nonlinear integral equations by projection-iteration methods. Nonlin. Vib. Probl. 25:1993;135-141.
28. Haneko H., Xu Yu. Degenerate kernel method for Hammerstein equations. Math. Comput. 56(193):1991;141-148.
29. Lardy L.J. A variation of Nyström's method for Hammerstein equations. J. Integral Equat. 3:1981;43-60.
30. Kumar S., Sloan I.H. A new collection type method for Hammerstein integral equations. Math. Comput. 48:1987;585-593.
31. Kumar S. A discrete collocation-type method for Hammerstein equations. SIAM J. Numer. Anal. 25:1988;328-341.
32. Aleksandrov V.M., Kovalenko E.V. Problems in Mechanics Media with Mixed Boundary Conditions. 1986;Nauka, Moscow.
33. M.A. Abdou, Fredholm-Volterra integral equation with singular kernel, Appl. Math. Comput. Ref. 7196, in press.
34. Abdou M.A., Mahmoud S.A., Darwish M.A. A numerical method for solving the Fredholm integral equation of the second kind. Korean J. Comput. Appl. Math. 5:1998;251-258.
35. Mkhitarian S.M., Abdou M.A. On different methods for solving Fredholm integral equation of the first kind with logarithmic kernel. Dokl. Acad, Nauk Armenia. 90:1989;1-10.
36. Frankel J.I. A Galerkin solution to a regularized Cauchy singular integro-differential equation. Quart. Appl. Math. LIII(2):1995;245-258.
37. Hachobusch W. Integral Equation Theory and Numerical Treatment. ISUM. vol. 120:1995.
38. Abdou M.A. Spectral relationships for integral operators in contact problem of impressing stamps. Appl. Math. Comput. 118:2001;95-111.
39. Abdou M.A. Fredholm integral equation of the second kind with potential kernel. J. Comput. Appl. Math. 72:1996;161-167.
40. Abdou M.A. Fredholm integral equation with potential kernel and its structure resolvent. Appl. Math. Comput. 107:2000;169-180.
41. Abdou M.A. Integral equation and contact problem for a system of impressing stamps. Appl. Math. Comput. 106:1999;141-148.
42. Gredshtein I.S., Ryzhik I.M. Tables of Integrals, Sums, Series and Products. fifth ed. 1980;Academic Press, New York.
43. Abdou M.A. Spectral relationships for integral operators in contact problem of impressing stamps. Appl. Math. Comput. 118:2001;95-111.
44. Abdou M.A. Integral equation with Macdonald kernel and its application to a system of contact problem. Appl. Math. Comput. 118:2001;83-94.