Analytical and numerical solution of a Fredholm equation of the first kind arising in an inverse refraction problem

Details Analytical and numerical solution of a Fredholm equation of the first kind arising in an inverse refraction problem Analytical and numerical solution of a Fredholm equation of the first kind arising in an inverse refraction problem

Mar 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985zvmmf..25..392p&link_type=abstract

Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki (ISSN 0044-4669), vol. 25, March 1985, p. 392-402. In Russian.

Mathematics

Fredholm Equations, Integral Transformations, Planetary Atmospheres, Radio Occultation, Radio Wave Refraction, Abel Function, Algorithms, Analytic Functions, Fourier Series, Fourier Transformation, Superposition (Mathematics), Uniqueness Theorem

Scientific paper

A solution is obtained to a Fredholm integral equation of the first kind arising in an inversion problem involving the radio-occultation investigation of a planetary atmosphere. The solution is a superposition of two Fourier cosine transformations and an Abel transformation, and can be used for the inversion of the Laplace and Mellin transformations and the generalized Stieltjes transformation in a finite region. Two numerical algorithms for determining the unknown function are examined, one of which is based on the analytical solution, while the other is based on the Fourier series expansion of the unknown function. Both algorithms are shown to yield a stable solution to the inverse problem.

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