Method for choosing the variable of integration on numerical simulation of ray paths in inhomogeneous media

An algorithm for solving the Cauchy problem by a numerical method by integrating with the selection of the variable of integration (the variable with respect to which the integration is performed) at each step. The application of the numerical simulation algorithm to the calculation of ray paths in inhomogeneous media in the geometrical optics approximation is presented. The testing and estimation of the accuracy of the algorithm are carried out using the example of a problem with a known analytical solution.