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Dixit, Sandeep; Singh, Om P.; Kumar, Sunil

A stable numerical inversion of generalized Abel’s integral equation. (English) Zbl 1241.65122

Appl. Numer. Math. 62, No. 5, 567-579 (2012).
Summary: A direct almost Bernstein operational matrix of integration is used to propose a stable algorithm for numerical inversion of the generalized Abel integral equation. The applicability of the earlier proposed methods was restricted to the numerical inversion of a part of the generalized Abel integral equation. The method is quite accurate and stable as illustrated by applying it to intensity data with and without random noise to invert and compare it with the known analytical inverse. Thus it is a good method for applying to experimental intensities distorted by noise.

Cited in 11 Documents

MSC:

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

Keywords:

Abel inversion; Bernstein polynomials; almost Bernstein operational matrix of integration; noise resistance; numerical examples; generalized Abel integral equation

Software:

Abel
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Full Text: DOI

References:

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