Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-25T09:12:07.270Z Has data issue: false hasContentIssue false
  • English
  • Français

A transformation of Cooke's treatment of some triple integral equations

Published online by Cambridge University Press:  17 February 2009

E. R. Love  and
D. L. Clements
E. R. Love
Affiliation:
Department of Mathematics, University of Melbourne, Melbourne, Australia.
D. L. Clements
Affiliation:
Department of Applied Mathematics, University of Adelaide, Adelaide, Australia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The reduction of an important class of triple integral equations to a pair of simultaneous Fredholm equations has been carried out by Cooke [1]. In this paper, Cooke's equations are transformed to new uncoupled Fredholm equations which, for certain important cases, are shown to be simpler than Cooke's and also superior for the purposes of solution by iteration.

Type
Research Article
Information
The ANZIAM Journal , Volume 19 , Issue 3 , June 1976 , pp. 259 - 288
Copyright
Copyright © Australian Mathematical Society 1976

References

[1]Cooke, J. C., ‘Some further triple integral equation solutions,’ Proc. Edinburgh Math. Soc. (II) 13 (1963), 303–316.CrossRefGoogle Scholar
[2]Noble, B., ‘The solution of Bessel function dual integral equations by a multiplying factor method,’ Proc. Camb. Phil. Soc. 59 (1963), 351–362.CrossRefGoogle Scholar
[3]Gubenko, V. S. and Mossakovskii, V. I., ‘Pressure of an axially symmetric circular die on an elastic half-space’, Prikl. Mat. Meh. 24 (1960), 330–334 (Russian);Google Scholar
translated as J. Appl. Math. Mech. 24 (1960), 477–486.CrossRefGoogle Scholar
[4]Williams, W. E., ‘Integral equation formulation of some three part boundary value problems,’ Proc. Edinburgh Math. Soc. (II) 13 (1963), 317–323.CrossRefGoogle Scholar
[5]Clements, D. L. and Love, E. R., ‘Potential problems involving an annulus,’ Proc. Camb. Phil. Soc. 76 (1974), 313–325.CrossRefGoogle Scholar
[6]Erdélyi, A. and others, ‘Higher Transcendental Functions,’ vol. 1, Bateman Manuscript Project (McGraw-Hill, 1953).Google Scholar
[7]Green, A. E. and Zerna, W., ‘Theoretical Elasticity’ (Oxford, 1954).Google Scholar