YNOGKM (Yun-Nan observatories geodesic in a Kerr-Newman spacetime for massive particles) performs fast calculation of time-like geodesics in the Kerr-Newman (K-N) spacetime; it is a direct extension of YNOGK (Yun-Nan observatories geodesic Kerr) calculating null geodesics in a Kerr spacetime. The four Boyer-Lindquis coordinates and proper time are expressed as functions of a parameter p semi-analytically by using the Weierstrass' and Jacobi's elliptic functions and integrals. The elliptic integrals are computed by Carlson's elliptic integral method, which guarantees the fast speed of the code. The source Fortran file ynogkm.f90 contains three modules: constants, rootfind, ellfunction, and blcoordinates.

Lemon solves the radiative transfer (RT) processes that contain scattering. These processes are described by differentio-integral equations with given initial or boundary conditions; Lemon solves these differentio-integral equations, which can be converted into the second kind integral equations of Fredholm. The code then obtains the Neumman solution (a series that consists of infinite terms of multiple integrals) from the Fredholm integral equation, and uses the Monte Carlo (MC) method to evaluate these integrals. Lemon is written in Fortran; IDL programs are included for plotting the results.