Numerical solution of Cauchy type singular integral equations by use of the Lobatto-Jacobi numerical integration rule

Nikolaos I. Ioakimidis; Pericles S. Theocaris

Aplikace matematiky (1978)

  • Volume: 23, Issue: 6, page 439-452
  • ISSN: 0862-7940

Abstract

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The Lobatto-Jacobi numerical integration rule can be extended so as to apply to the numerical evaluation of Cauchy type principal value integrals and the numerical solution of singular intergral equations with Cauchy type kernels by reduction to systems of linear equations. To this end, the integrals in such a singular integral equation are replaced by sums, as if they were regular integrals, after the singular integral equation is applied at appropriately selected points of the integration interval. An application of this method of numerical solution of singular integral equations is made in the case of a problem of the theory of plane elasticity.

How to cite

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Ioakimidis, Nikolaos I., and Theocaris, Pericles S.. "Numerical solution of Cauchy type singular integral equations by use of the Lobatto-Jacobi numerical integration rule." Aplikace matematiky 23.6 (1978): 439-452. <http://eudml.org/doc/15072>.

@article{Ioakimidis1978,
abstract = {The Lobatto-Jacobi numerical integration rule can be extended so as to apply to the numerical evaluation of Cauchy type principal value integrals and the numerical solution of singular intergral equations with Cauchy type kernels by reduction to systems of linear equations. To this end, the integrals in such a singular integral equation are replaced by sums, as if they were regular integrals, after the singular integral equation is applied at appropriately selected points of the integration interval. An application of this method of numerical solution of singular integral equations is made in the case of a problem of the theory of plane elasticity.},
author = {Ioakimidis, Nikolaos I., Theocaris, Pericles S.},
journal = {Aplikace matematiky},
keywords = {Lobatto-Jacobi numerical integration rule; Cauchy type principal value integrals; singular integral equations; Cauchy type kernels; Lobatto-Jacobi numerical integration rule; Cauchy type principal value integrals; singular integral equations; Cauchy type kernels},
language = {eng},
number = {6},
pages = {439-452},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Numerical solution of Cauchy type singular integral equations by use of the Lobatto-Jacobi numerical integration rule},
url = {http://eudml.org/doc/15072},
volume = {23},
year = {1978},
}

TY - JOUR
AU - Ioakimidis, Nikolaos I.
AU - Theocaris, Pericles S.
TI - Numerical solution of Cauchy type singular integral equations by use of the Lobatto-Jacobi numerical integration rule
JO - Aplikace matematiky
PY - 1978
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 23
IS - 6
SP - 439
EP - 452
AB - The Lobatto-Jacobi numerical integration rule can be extended so as to apply to the numerical evaluation of Cauchy type principal value integrals and the numerical solution of singular intergral equations with Cauchy type kernels by reduction to systems of linear equations. To this end, the integrals in such a singular integral equation are replaced by sums, as if they were regular integrals, after the singular integral equation is applied at appropriately selected points of the integration interval. An application of this method of numerical solution of singular integral equations is made in the case of a problem of the theory of plane elasticity.
LA - eng
KW - Lobatto-Jacobi numerical integration rule; Cauchy type principal value integrals; singular integral equations; Cauchy type kernels; Lobatto-Jacobi numerical integration rule; Cauchy type principal value integrals; singular integral equations; Cauchy type kernels
UR - http://eudml.org/doc/15072
ER -

References

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  1. P. S. Theocaris, N. I. Ioakimidis, On the Gauss-Jacobi Numerical Integration Method Applied to the Solution of Singular Integral Equations, To appear in the "Bulletin of the Calcutta Mathematical Society", 1979. (1979) Zbl0429.65115MR0583924
  2. Z. Kopal, Numerical Analysis, Chapman and Hall, London, 1961. (1961) Zbl0101.33701
  3. P. S. Theocaris, N. I. Ioakimidis, Numerical Integration Methods for the Solution of Singular Integral Equations, Quarterly of Applied Mathematics, 1977, Vol.35, 173-183. (1977) Zbl0353.45016MR0445873
  4. P. S. Theocaris, N. I. Ioakimidis, Application of the Gauss, Radau and Lobatto Numerical Integration Rules to the Solution of Singular Integral Equations, To appear in the "Zeitschrift für angewandte Mathemaiik und Mechanik", 1978. (1978) Zbl0399.65095MR0516804
  5. N. I. Ioakimidis, P. S. Theocaris, On the Numerical Solution of a Class of Singular Integral Equations, Journal of Mathematical and Physical Sciences, 1977, Vol. 11, pp. 219-235. (1977) Zbl0353.45016MR0483590
  6. N. I. Ioakimidis, P. S. Theocaris, On the Numerical Evaluation of Cauchy Principal Value Integrals, Revue Roumaine des Sciences Techniques- Série de Mécanique Appliquée, 1977, Vol. 22 pp. 803-818. (1977) Zbl0376.65009MR0483321
  7. F. D. Gakhov, Boundary Value Problems, Pergamon Press, Oxford, 1966 [Translation of: Krayevye Zadachi, Fizmatgiz, Moscow, 1963]. (1966) Zbl0141.08001MR0198152
  8. G. Szegö, Orthogonal Polynomials, (revised edition). American Mathematical Society, New York, 1959. (1959) Zbl0089.27501MR0106295
  9. D. Elliott, 10.1090/S0025-5718-1971-0294737-5, Mathematics of Computation, 1971, Vol. 25, No 114, pp. 309-315. (1971) Zbl0221.65027MR0294737DOI10.1090/S0025-5718-1971-0294737-5
  10. A. Erdélyi(ed.), al., Higher Transcendental Functions, Vol. II, McGraw-Hill, New York, 1953. (1953) Zbl0052.29502
  11. F. Erdogan G. D. Gupta, T. S. Cook, Numerical Solution of Singular Integral Equations, In: Mechanics of Fracture, Vol. 1: Methods of Analysis and Solutions of Crack Problems (edited by G. C. Sih). Noordhoff, Leyden, the Netherlands, 1973, Chap. 7, pp. 368--425. (1973) Zbl0265.73083MR0471394
  12. M. B. Porter, On the Roots of the Hypergeometric and Bessel's Functions, American Journal of Mathematics, 1898, Vol. 20, pp. 193-214. Zbl29.0402.01MR1505769
  13. T. S. Cook, F. Erdogan, 10.1016/0020-7225(72)90063-8, International Journal of Engineering Science,, 1972, Vol. 10, pp. 677-697. (1972) Zbl0237.73096DOI10.1016/0020-7225(72)90063-8
  14. F. Erdogan, T. S. Cook, 10.1007/BF00113928, International Journal of Fracture, 1974, Vol. 10, pp. 227-240. (1974) DOI10.1007/BF00113928
  15. K. Y. Lin, J. W. Mar, Finite Element Analysis of Stress Intensity Factors for Cracks at a Bi-Material Interface, International Journal of Fracture, 1976, Vol. 12, pp. 521-531. (1976) 
  16. E. Smith, A Pile-up of Dislocations in a Bi-Metallic Solid, Scripta Metallurgica, 1969, Vol. 3, pp. 415-418. (1969) 
  17. T. W. Chou, Dislocation Pileups and Elastic Cracks at a Bimaterial Interface, Metallurgical Transactions, 1970, Vol. 1, pp. 1245-1248. (1970) 

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