DELO-Bezier formal solutions of the polarized radiative transfer equation

We present two new accurate and efficient method to compute the formal solution of the polarized radiative transfer equation. In this work, the source function and the absorption matrix are approximated using quadratic and cubic Bezier spline interpolants. These schemes provide 2nd and 3rd order approximation respectively and don't suffer from erratic behavior of the polynomial approximation (overshooting). The accuracy and the convergence of the new method are studied along with other popular solutions of the radiative transfer equation, using stellar atmospheres with strong gradients in the line-of-sight velocity and in the magnetic-field vector.