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Two numerical methods for Abel's integral equation with comparison

Abstract : Analogy between Abel's integral equation and the integral of fractional order of a given function, j^α f(t), is discussed. Two different numerical methods are presented and an approximate formula for j^α f(t) is obtained. The first approach considers the case when the function, f(t), is smooth and a quadrature formula is obtained. A modified formula is deduced in case the function has one or more simple pole. In the second approach, a procedure is presented to weaken the singularities. Both two approaches could be used to solve numerically Abel's integral equation. Some numerical examples are given to illustrate our results.
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Abdallah Ali Badr. Two numerical methods for Abel's integral equation with comparison. Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées, INRIA, 2012, Volume 15, 2012, pp.1-10. ⟨10.46298/arima.1955⟩. ⟨hal-01299497⟩

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