Analytical description for application of 1D Kohonen scheme for constructing adaptive meshes

In this paper, the analysis of analytical approaches to investigation of an asymptotical disposition for a special iterative discrete-stochastic algorithm for constructing adaptive meshes using the Kohonen self-organizing maps is made. For a simplified one-dimensional case, a “recurrent” approach to obtaining mean most probable dispositions of grid nodes for a small number of iterations has been developed. This approach allows one to conduct interesting analytical investigations and numerical testing for the algorithm considered.