SOLUTION TO A CLASS OF SINGULAR INTEGRAL EQUATIONS OCCURRING IN MATHEMATICAL PHYSICS (thesis)

Technical Report · Mon Aug 01 04:00:00 EDT 1960

OSTI ID:4142603

Hinchey, F A

A Fourier series solution is developed for a class of singular integral equations that arise in various problems of mathematical physics. This class of integral equations is closely related to certain Wiener-Hopf type equations on the finite range. A brief review of the Wiener-Hopf technique is included as general background. A solution to a similar class of equations on the finite range is given, and the disadvantages of this technique for the solution of a more extended class of equations are pointed out. The first application of this technique that is considered is the problem of the cylindrical antenna. Numerical results are obtained for half and full wavelength center-fed antennas with half length to radius ratios of 60 and 500 pi . These results are shown to agree with King-Middleton iterative results to within approximately 2%. The second example considered is the problem of the diffusion of neutrons through an infinite plate of finite thickness. No numerical results are obtained for this problem. However, the integral equation is formulated and the solution indicated. (auth)

• Research Organization: Sandia Corp., Albuquerque, N. Mex.
• NSA Number: NSA-14-024462
• OSTI ID: 4142603
• Report Number(s): SCTM-259-60(14)
• Country of Publication: United States
• Language: English

Related Subjects

CYLINDERS
DIFFUSION
ELECTRONIC EQUIPMENT
EQUATIONS
FOURIER SERIES
INTEGRALS
MATHEMATICS
MATHEMATICS AND COMPUTERS
NEUTRONS
NUMERICALS
PLATES
WIENER-HOPF METHOD