2012/12/12 by J. de la Cruz Rodríguez, N. Piskunov · 3 citations
Mathematics · Physics and Astronomy · #Applied mathematics #Astrophysics and Star Formation Studies #Bézier curve #Geometry #Mathematical analysis #Mathematics #Optics #Physics #Polynomial #Quadratic equation #Radiative transfer #Solar and Space Plasma Dynamics #Spline (mechanical) #Stellar, planetary, and galactic studies #Thermodynamics #astro-ph.IM #astro-ph.SR
paper · pdf · doi:10.1088/0004-637x/764/1/33
Accepted for publication in ApJ
arxiv created 2012/12/12 · openalex publication_date 2013/01/23 · arxiv updated 2015/06/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We present two new accurate and efficient methods 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 second- and third-order approximations, respectively, and do not 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.