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Application of modified moments in the numerical solution of the Abel integral equation. (English) Zbl 0575.65138

R. Piessens and P. Verbaeten [BIT 13, 451-457 (1973; Zbl 0266.65081)] have described a method for the numerical solution of the Abel integral equation, using Laplace transform techniques. The present paper shows how this powerful method can be modified to save a substantial portion of computational work. The modification is based on the application of modified moments (certain integrals involving Chebyshev polynomials of the second kind) which are computed by using a simple recurrence relation.

MSC:

65R20 Numerical methods for integral equations
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)

Citations:

Zbl 0266.65081
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