This is a method that has been primarily used to study radiative transfer in the photospheres of stars and was originally described by Hummer & Rybicki [14]. The main difference between this method and the other methods described here is that rather than trying to solve the radiative transfer equation by integrating it, the solution is sought by considering the differential form of the equation. By using the finite difference method (sometimes also referred to as the Feautrier method3.2) it is possible to solve the differential equation with its boundary conditions. Hummer & Rybicki consider this a more efficient way of considering the problem in their 1971 paper. However Rybicki then chose not to pursue the method and his later papers concentrate on the integral method. The main problem with the method is that it is less intuitive than the integral method which is also much easier to test. This is because the integral method can be easily checked at each integration step whereas the differential method relies on the maths being correctly programmed to yield a final answer. Nonetheless the method has been used successfully by others (eg. Mihalas [21]) and the resulting program known as MULTIMOL has been used by J.Yates (private communication) to check the results from the Stenholm program.