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

arima:1955 - Revue Africaine de 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]


    Consultation statistics

    This page has been seen 176 times.
    This article's PDF has been downloaded 206 times.