On a certain approach to modeling dynamic systems

When developing complexes of computer programs modeling various dynamic systems, it is often required to build mathematical models of a particular subject area. In the article we constructed such functions that it is possible to construct a superposition of functions (term) for any given programming language. Calculating the above term generates a computational process that occurs when the program is executed. If the program is designed to model a dynamic system, then the calculation of the algebraic term is an adequate simulation for the dynamic system functioning. Thus, an algebraic model of a programming language is developed for modeling of dynamic systems, where calculation of algebraic terms generates modeling process of dynamical systems. To construct these functions, it is necessary to accurately describe the domain of definition and the range of values of these functions. To construct domains of definition and ranges of values for these functions we used context-free grammars, and identification operation. In addition to these tools, the concept of a multi-level model, the concept of indirect naming (indirect addressing), recursion, and also some simple tools from the theory of algorithms and programming theory are used. Thus, a method of computer modeling of various dynamic systems, where an arbitrary program can be represented as an algebraic term of a universal algebra with a signature from the indicated functions, is found to be sufficiently broad in practical coverage.