  We propose the generalized quadrature methods for numerical solution of
singular integral equation of Abel type. We overcome the singularity using the
analytical calculation of the singular integral expression. The problem of
solution of singular integral equation is reduced to nonsingular system of
linear algebraic equations without shift meshes techniques employment. We also
propose generalized quadrature method for solution of Abel equation using the
singular integral. Relaxed errors bounds are derived. In order to improve the
accuracy we use Tikhonov regularization method. We demonstrate the efficiency
of proposed techniques on infrared tomography problem. Numerical experiments
show that it make sense to apply regularization in case of highly noisy sources
only. That is due to the fact that singular integral equations enjoy
selfregularization property.
