V. K. Singh, R. K. Pandey and O. P. Singh, “New Stable Numerical Solution of Singular Integral Equations of Abel Type by Using Normalized Bernstein Polynomials,” Applied Mathematical Sciences, Vol. 3, No. 5, 2009, pp. 241-255.

has been cited by the following article:

• TITLE: Generalized Abel Inversion Using Homotopy Perturbation Method

  AUTHORS: Sunil Kumar, Om P. Singh, Sandeep Dixit

  KEYWORDS: Generalized Abel Integral Equation, Homotopy Perturbation Method, Noise Term, Stability

  JOURNAL NAME: Applied Mathematics, Vol.2 No.2, February 25, 2011

  ABSTRACT: Many problems in physics like reconstruction of the radially distributed emissivity from the line-of-sight projected intensity, the 3-D image reconstruction from cone beam projections in computerized tomography, etc. lead naturally, in the case of radial symmetry, to the study of Abel’s type integral equation. Obtaining the physically relevant quantity from the measured one requires, therefore the inversion of the Abel’s integral equation. The aim of this letter is to present a user friendly algorithm to invert generalized Abel integral equation by using homotopy perturbation method. The stability of the algorithm is analysed. The validity and applicability of this powerful technique is illustrated through various particular cases which demonstrate its efficiency and simplicity in solving these types of integral equations.