ANALYTICAL SOLUTION OF THE HILBERT SINGULAR INTEGRAL EQUATION WITH RESPECT TO THE HILBERT FORMULA

M.  Sifuzzaman; M.S  Uddin; M. A.  Hakim; M. A.  Hossen; M. A.  Mamun

doi:10.53808/KUS.2008.9.2.0807-PS

Authors

M. Sifuzzaman Mathematics Discipline, Khulna University, Khulna-9208, Bangladesh
M.S Uddin Mathematics Discipline, Khulna University, Khulna-9208, Bangladesh
M. A. Hakim Department of Mathematics, Comilla University, Comilla-3500, Bangladesh
M. A. Hossen Department of Mathematics, Comilla University, Comilla-3500, Bangladesh
M. A. Mamun Mathematics Discipline, Khulna University, Khulna-9208, Bangladesh

DOI:

https://doi.org/10.53808/KUS.2008.9.2.0807-PS

Keywords:

Fredholm integral equation, Hilbert formula, kernel

Abstract

The objective of this paper is to solve the Hilbert singular integral equation of first and second kind by using the Hilbert formula and some known results are obtained as special cases. Applications of these singular integral equations to Boundary value problems of Elasticity and allied subjects are well known.

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References

Chakrabarti, A. 1986. A tractable Pair of the Cauchy Singular Integral Equation. J. Ind. Inst. Sci., 66: 331-326.

Jeffry, P. A. 1976. Integral Equations. International Textbook Company Ltd., London.

Mikhlin, S.G. 1957. Integral Equations. Pergamon, Oxford, England.

Pennline, J. A. 1976. A More Tractable Solution to a Singular Integral Equaton Obtained by Solving a Related Hilbert Problem for Two Unknowns. J. Res. Bur. Stds., 80B(3): 403-414.

Muskhelishvilli, N. I. 1953. Singular Integral Equations. Noordhoff, Gronningen, Holland.

Peters, A. S. 1972. Pairs of Cauchy Singular Integral Equations. Comm. Pure Applied Mathematics, 25: 369-402.

Pogorzelski, W. 1966. Integral Equations and their Applications. Pergamon, Oxford, England.

Swarup, S. 1996. Integral Equations. Krishna Prakashana Media Ltd., India.

Tricomi, F.G. 1957. Integral Equations. Interscience, New York.

Widom, H. 1969. Lectures on Integral Equations. Van Nostrand-Reinhold New York.

Williams, W.E. 1978. Note on a Singular Integral Equation. J. Inst. Maths. Applics., 22: 211-241.

Wirda, G. 1930. Integral Equations, Leipzig, Germany.