Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

A numerical technique for the solution of singular integral equations of the second kind


Authors: G. R. Miller and L. M. Keer
Journal: Quart. Appl. Math. 42 (1985), 455-465
MSC: Primary 65R20
DOI: https://doi.org/10.1090/qam/766882
Correction: Quart. Appl. Math. 43 (1985), 127.
MathSciNet review: 766882
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A numerical technique for the solution of singular integral equations of the second kind is presented. The technique extends the piecewise quadratic method used by Gerasoulis [6], to solve singular integral equations of the first kind. Quadrature formulae are derived in terms of infinite series and are used to reduce the integral equation to a set of linear algebraic equations. Two numerical examples are given, and the results are compared with exact solutions.


References [Enhancements On Off] (What's this?)

  • [1] F. Erdogan and G. Gupta, On the numerical solution of singular integral equations, Quart. Appl. Math. 30, 525-534 (1972) MR 0408277
  • [2] S. Krenk, On quadrature formulas for singular integral equations of the first and second kind, Quart. Appl. Math. 33, 225-232 (1975) MR 0448967
  • [3] P. S. Theocaris, and N. I. Iokimidis, Numerical integration methods for the solution of singular integral equations, Quart. Appl. Math. 35, 173-182 (1977) MR 0445873
  • [4] A. Gerasoulis, and R. P. Srivastav, A method for the numerical solution of singular integral equations with a principal value integral, Int. J. of Engn. Sci. 19, 1293-1293 (1981) MR 660561
  • [5] A. Gerasoulis, Piecewise polynomial approximations in the solution of singular integral equations, in Advances in Computer Methods for Partial Differential Equations, R. Vichnevetsky and R. S. Stepleman, eds., MACS 1981, 386-390
  • [6] A. Gerasoulis, The use of piecewise quadratic polynomials for the solution of singular integral equations of Cauchy type, Comp. and Math. with Appl. 8, 15-22 (1982) MR 644546
  • [7] N. I. Muskhelishvili, Singular integral equations, 2nd ed., P. Noordhoff, Groningen, 1953 MR 0355494
  • [8] E. R. Hansen, A table of series and products, Prentice-Hall, Ind., Englewood Cliffs, New Jersey, 1975
  • [9] K. Knopp, Theory and application of infinite series, Blackie and Son Ltd, London, 1928
  • [10] C. Jordan, Calculus of finite differences, 3rd ed., Chelsea Publishing Co. New York, 1965, 327 MR 0183987
  • [11] W. H. Beyer, ed., CRC standard mathematical tables, 25th ed., CRC Press, Inc., Boca Raton, Florida, 1973

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 65R20

Retrieve articles in all journals with MSC: 65R20


Additional Information

DOI: https://doi.org/10.1090/qam/766882
Article copyright: © Copyright 1985 American Mathematical Society

American Mathematical Society