Method of Computer Analogy and Its Applications

Abstract

This paper further develops a previously proposed method of computer analogy, based on the formalization of core computational properties: a finite number of digits and the transfer from one rank to another. Aimed at constructing new analytical solutions for nonlinear differential systems, the key outcome of this method is semi-analytical solution. We obtained new results compared to our earlier publications. Namely, the construction of an analytical solution was demonstrated for Carleman kinetic system. Two semi-analytical approximations are proposed for the Van der Pol equation, reduced to a system of two nonlinear equations. The semi-analytical approximation derived for the Shimizu-Morioka system—based on the probabilistic properties of the coefficients of the highest-degree terms—demonstrates the presence of a strange attractor.