Abdallah Ali Badr - Two numerical methods for Abel's integral equation with comparison

arima:1955 - Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées, August 26, 2012, Volume 15, 2012 - https://doi.org/10.46298/arima.1955
Two numerical methods for Abel's integral equation with comparison

Authors: Abdallah Ali Badr

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.

Volume: Volume 15, 2012
Published on: August 26, 2012
Submitted on: February 17, 2012
Keywords: Abel's integral equation, fractional integrals, Jacobi polynomials, Gauss-Jacobi quadrature formula.,[INFO] Computer Science [cs],[MATH] Mathematics [math]


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