Hostname: page-component-848d4c4894-8kt4b Total loading time: 0 Render date: 2024-06-20T09:12:48.241Z Has data issue: false hasContentIssue false

The solution of some integral equations

Published online by Cambridge University Press:  17 February 2009

John F. Ahner
Affiliation:
Department of Mathematics, Vanderbilt University, Nashville, Tennesse 37235, U.S.A.
John S. Lowndes
Affiliation:
Department of Mathematics, University of Strathclyde, Glasgow G1 1XH, U.K.
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.

Algorithms are developed by means of which certain connected pairs of Fredholm integral equations of the first and second kinds can be converted into Fredholm integral equations of the second kind. The methods are then used to obtain the solutions of two different sets of triple integral equations tht occur in mixed boundary value problems involving Laplace' equation and the wave equation respectively.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Ahner, J. F. and Lowndes, J. S., “On the solution of a class of integral equations”, J. Math. Anal. Appl. 100 (1984) 447462.Google Scholar
[2]Ahner, J. F. and Lowndes, J. S., “On the solution of a class of integral equations II”, J. Math. Anal. Appl. 110 (1985) 391406.Google Scholar
[3]Lowndes, J. S., “On dual and triple integral equations involving modified Bessel functions”, Appl. Anal. 6 (1977) 253260.Google Scholar
[4]Lowndes, J. S., “The solution of some integral equations”, Math. Methods Appl. Sci. 2 (1979) 2633.Google Scholar
[5]Magnus, W., Oberhettinger, F. and Soni, R. P., Formulas and theorems for the special functions of mathematical physics, 3rd ed. (Springer-Verlag, 1966).Google Scholar
[6]Sneddon, I. N., Mixed boundary value problems in potential theory (North Holland, 1966).Google Scholar
[7]Williams, W. E., “A class of integral equations”, Proc. Camb. Phil. Soc. 59 (1963) 589597.CrossRefGoogle Scholar