Generalized Abel Inversion Using Extended Hat Functions Operational Matrix

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 eithera(y)=0orb(y)=0.