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Solution of the Generalized Abel Integral Equation by Using Almost Bernstein Operational Matrix
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American Journal of Computational Mathematics·Volume 01 (2011)·Pages 226–234·Published 22 December 2011·DOI10.4236/ajcm.2011.14026
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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.
KeywordsAbel InversionBernstein PolynomialsAlmost Bernstein Operational Matrix Of IntegrationNoise Resistance
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