Preconditioned Bi-Conjugate Gradient Method for Radiative Transfer in Spherical Media

A robust numerical method called the Preconditioned Bi-Conjugate Gradient (Pre-BiCG)method is proposed for the solution of radiative transfer equation in spherical geometry.A variant of this method called Stabilized Preconditioned Bi-Conjugate Gradient (Pre-BiCG-STAB) is also presented. These are iterative methods based on the construction of a set of bi-orthogonal vectors. The application of Pre-BiCG method in some benchmark tests show that the method is quite versatile, and can handle hard problems that may arise in astrophysical radiative transfer theory.