Advertisement

Solution of singular integral equations with logarithmic and Cauchy kernels

  • A Chakrabarti
  • T Sahoo
Article
  • 78 Downloads

Abstract

A direct method of solution is presented for singular integral equations of the first kind, involving the combination of a logarithmic and a Cauchy type singularity. Two typical cases are considered, in one of which the range of integration is a single finite interval and, in the other, the range of integration is a union of disjoint finite intervals. More such general equations associated with a finite number (greater than two) of finite, disjoint, intervals can also be handled by the technique employed here.

Keywords

Water waves scattering Cauchy kernel logarithmic kernel 

References

  1. [1]
    Muskhelishvili N I,Singular integral equation (Noordhoof, Holland) (1963)Google Scholar
  2. [2]
    Ursell F, The effect of a fixed vertical barrier on surface waves in deep water,Proc. Camb. Phil. Soc. 43 (1947) 374–382zbMATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    Mandal B N, A note on the diffraction of water waves by a vertical wall with a gap,Arch. Mech. 39 (1987) 269–273Google Scholar
  4. [4]
    Gakhov F D,Boundary value problems (Dover Publications: New York) (1990)zbMATHGoogle Scholar
  5. [5]
    Chakrabarti A and George A J, Solution of a singular integral equation involving two intervals arising in the theory of water waves,Appl. Math. Lett. 7(5) (1994) 43–47zbMATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    Banerjea S and Mandal B N, On a singular integral equation with logarithmic and Cauchy kernel,Int'l J. Math. Educ. Sci. Technol. 26(2) (1995) 267–313CrossRefGoogle Scholar

Copyright information

© Indian Academy of Sciences 1996

Authors and Affiliations

  • A Chakrabarti
    • 1
  • T Sahoo
    • 1
  1. 1.Department of MathematicsIndian Institute of ScienceBangaloreIndia

Personalised recommendations