Abstract
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.
Highlights
Abel’s integral equation [1] occurs in many branches of science
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
Summary
Abel’s integral equation [1] occurs in many branches of science. Usually, physical quantities accessible to measurement are quite often related to physically important but experimentally inaccessible ones by Abel’s integral equation. Some of the examples are: microscopy [2], seismology [3,4], radio astronomy [5], satellite photometry of airglows [6], electron emission [7], atomic scattering [8], radar ranging [9], and optical fiber evaluation [10,11,12]. Chakrabarti [20] employed a direct function theoretic method to determine the closed form solution of the following generalized Abel integral equation a.
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