Lewanowicz, S. Application of modified moments in the numerical solution of the Abel integral equation. (English) Zbl 0575.65138 Zastosow. Mat. 18, 311-317 (1984). 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) Keywords:Abel integral equation; Laplace transform techniques; modified moments; Chebyshev polynomials; recurrence relation Citations:Zbl 0266.65081 PDFBibTeX XMLCite \textit{S. Lewanowicz}, Zastosow. Mat. 18, 311--317 (1984; Zbl 0575.65138)