TY - JOUR
A2 - Robert, Frédéric
AU - Tripathi, Manoj P.
AU - Pandey, Ram K.
AU - Baranwal, Vipul K.
AU - Singh, Om P.
PY - 2013
DA - 2013/05/19
TI - Generalized Abel Inversion Using Extended Hat Functions Operational Matrix
SP - 652541
VL - 2013
AB - Abel type integral equations play a vital role in the study of compressible flows around axially symmetric bodies. The relationship between emissivity and the measured intensity, as measured from the outside cylindrically symmetric, optically thin extended radiation source, is given by this equation as well. The aim of the present paper is to propose a stable algorithm for the numerical inversion of the following generalized Abel integral equation: I(y)=a(y)∫αy((rμ-1ε(r))/(yμ-rμ)γ)dr+b(y)∫yβ((rμ-1ε(r)) /(rμ-yμ)γ)dr, α≤y≤β, 0<γ<1, using our newly constructed extended hat functions operational matrix of integration, and give an error analysis of the algorithm. The earlier numerical inversions available for the above equation assumed either a(y)=0 or b(y)=0.
SN - 2314-498X
UR - https://doi.org/10.1155/2013/652541
DO - 10.1155/2013/652541
JF - International Journal of Analysis
PB - Hindawi Publishing Corporation
KW -
ER -