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A Cauchy problem for Milne's integral equation with a pincherle-goursat kernel

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Abstract

In a series of our preceding papers (cf. Bellman and Ueno, 1971a, 1971b, 1972a, 1972b, 1972c; Ueno 1972), with the aid of invariant imbedding technique, we transformed the two point boundary value problem for integral equations into the initial-value problem. In this paper, extending the procedure to the Milne's integral equation, whose kernel is expanded into a double Fourier cosine series, we show how to find a Cauchy system for the required solution of Milne's integral equation and the Fredholm resolvent. The obtained integro-differential equations are reduced to large system of ordinary differential equations with known initial conditions. Then, they are suitable for the numerical computation of the solution by the modern high-speed computer.

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  1. S. Ueno

    Present address: Research Institute for Information Science, Kanazawa Institute of Technology, Ogigaoka Nonoichi, Ishikawa, Japan

Authors and Affiliations

  1. Dept. of Electrical Engineering, University of Southern California, Los Angeles, Calif., USA

    S. Ueno

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  1. S. Ueno
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Ueno, S. A Cauchy problem for Milne's integral equation with a pincherle-goursat kernel. Astrophys Space Sci 44, 151–158 (1976). https://doi.org/10.1007/BF00650479

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  • DOI: https://doi.org/10.1007/BF00650479

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