The accuracy of various models used to study inverse saturable absorbers is investigated in this paper. An exact solution of the problem of propagation of laser radiation through a medium with reverse saturable absorption is presented for the case of propagation of light signals with energy equal to the saturation energy in media without relaxation. We consider the case when a pulse of Gaussian shape. With an exact solution, the result of a numerical calculation of the transport equation and Bouguer's law is compared for the intensity of the accuracy realized by different methods of different accuracy. The paper is considered very small extent environment compared with the linear dimensions pulse. Schemes 1-4 of the order of accuracy for these two equations are constructed. For eight different schemes, approximation errors are given. It is shown that already with the use of third-order schemes for a laser pulse of 0.1 J the numerical solution differs from the exact one by only a few nanojoules. Thus, when studying the effect of RSA in large-sized carbon particles, substances where the effect is observed only at energies <1J, the use of third- and fourth-order methods may be unnecessary, especially when using a rather small step.

Keywords: numerical methods, transport equation, approximation, reverse saturable absorption