Modeling of Nonlinear Environment with the Help of Families of the Atomic Functions

Abstract

The procedure of constructing families of the atomic radial basis functions, which are recommended to be used to account for the heterogeneity of the environment in the simulation ofphysical processes is been considered. The solution of corresponding boundary problems are performed by meshless scheme, and the atomic functions are selected which satisfy the requirements. The families of infinitely differentiable compactly supported functions that are solutions of functional differential equations of special type had been considered. Expansion of classes of the atomic functions of several variables and expanding their properties considered is constructing a family of atomic radial basis functions of three independent variables on the example of the special type functionally-differentional equations. It should be noted that the support region is dependent on the compression ratio and can be specified in processes of construction solutions to provide the corresponding properties of the desired functions.