SOFTWARE IMPLEMENTATION OF ASYMPTOTIC METHODS IN MAXIMA FOR INTELLIGENT SYSTEMS FOR ANALYSIS AND PREDICTION OF OBJECT MOTION IN A DYNAMIC ENVIRONMENT

Abstract

The article considers the application of the computer algebra system Maxima for automating the construction of asymptotic solutions of differential equations with a small parameter. Asymptotic methods are among the most tools for analyzing complex dynamic systems, but their practical use is complicated by the large amount of cumbersome algebraic and differential transformations. The proposed approach makes it possible to automate these procedures and minimize the probability of errors that usually occur during manual calculations. A software module has been developed that implements an algorithm for generating a system of equations for expansion coefficients, performs sorting of expressions by the powers of a small parameter, and provides simplification of analytical results using user-defined substitution rules.To demonstrate the capabilities of the developed module, an example of an equation describing the motion of an object in a variable force field is considered. The obtained results confirm that automation enables efficient work with higher-order expansions, where the complexity of expressions grows exponentially. The presented experimental data (computation time, number of terms in expressions) illustrate the advantages of the proposed approach. A specific feature of the module is the ability to switch between different representations of results, in particular from exponential to trigonometric form, which makes expressions more compact and convenient for further processing.The scientific novelty of the work lies in the integration of asymptotic methods with Maxima as a symbolic tool for building analytical models suitable for use as a core of intelligent systems for motion prediction in dynamic environments. The practical significance is defined by the possibility of integrating the module into digital twins, robotic systems, and transport platforms, where the accuracy and speed of prediction are critical.Possible directions for future research include the development of strategies to reduce the symbolic complexity of expressions, the application of hybrid symbolic-numerical methods, as well as the integration of the module with neural network subsystems to enable real-time prediction and validation.