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
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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.
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W. H. Beyer, ed., CRC standard mathematical tables, 25th ed., CRC Press, Inc., Boca Raton, Florida, 1973
F. Erdogan and G. Gupta, On the numerical solution of singular integral equations, Quart. Appl. Math. 30, 525–534 (1972)
S. Krenk, On quadrature formulas for singular integral equations of the first and second kind, Quart. Appl. Math. 33, 225–232 (1975)
P. S. Theocaris, and N. I. Iokimidis, Numerical integration methods for the solution of singular integral equations, Quart. Appl. Math. 35, 173–182 (1977)
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)
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
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)
N. I. Muskhelishvili, Singular integral equations, 2nd ed., P. Noordhoff, Groningen, 1953
E. R. Hansen, A table of series and products, Prentice-Hall, Ind., Englewood Cliffs, New Jersey, 1975
K. Knopp, Theory and application of infinite series, Blackie and Son Ltd, London, 1928
C. Jordan, Calculus of finite differences, 3rd ed., Chelsea Publishing Co. New York, 1965, 327
W. H. Beyer, ed., CRC standard mathematical tables, 25th ed., CRC Press, Inc., Boca Raton, Florida, 1973
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Article copyright:
© Copyright 1985
American Mathematical Society
