Monte Carlo methods refers to numerical procedures for solving mathematical problems by modelling of random variables. One can apply this approach to mathematical problems of any kind. General mathematical methods are exemplified by the successful application of Monte Carlo simulations especially when applied to Astrophysical problems. One of the problems that I am working on is the flows around black holes. The most celebrated model to explain the spectrum for these was the Shakura-Sunyaev cool disk model. But this could not explain the high energy power law tail present in the spectrum until 1976, when Shapiro explained that Comptonisation of low-frequency photons present in the accretion disk gives rise to this high energy power-law tail. Though a lot of work has been done analytically to get an order of magnitude estimate of the Comptonisation present in a given system but the spectra can be modelled more accurately by the Monte Carlo simulations which allows the natural interaction between the photons and electrons present in the system. In this talk I will :
(1) Mainly focus on general Monte Carlo methods
(2) How to model Astrophysical systems using this method
(3) Present preliminary results of including Monte Carlo simulations in flows around Black Holes.