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Radiative transfer (RT) problems in which the source function includes ascattering-like integral are typical two-points boundary problems. Theirsolution via differential equations implies to make hypotheses on the solutionitself, namely the specific intensity I(tau;n) of the radiation field. On thecontrary, integral methods require to make hypotheses on the source functionS(tau). It looks of course more reasonable to make hypotheses on the latterbecause one can expect that the run of S(tau) with depth be smoother than thatof I(tau;n).  In previous works we assumed a piece-wise parabolic approximation for thesource function, which warrants the continuity of S(tau) and its firstderivative at each depth point. Here we impose the continuity of the secondderivative S"(tau). In other words, we adopt a cubic spline representation tothe source function, which highly stabilize the numerical processes.

An improved version of the Implicit Integral Method to solving radiative transfer problems