FEATURES OF THE IMPLEMENTATION OF INTEGRAL MODELS RESEARCH TOOLS IN THE MATLAB SYSTEM

Abstract

The computer mathematics system MATLAB provides many opportunities for conducting various studies. However, it lacks inbuild tools of solving integral equations and their systems. Numerical implementations of systems of Volterra integral equations require a significant number of calculations and may require large data sets to store the results of calculations, which requires optimal use of memory and the most efficient organization of calculations in MATLAB modules. The work systematizes approaches to creating modules for the MATLAB system expansion for computational tasks of various directions, describes the ways of building efficient modules according to the criteria of memory optimization and calculation speed. The procedure for conducting studies of integral models of dynamic systems using MATLAB functions is proposed and the designed modules for solving Volterra integral equations and their systems by direct methods of approximate solution are described. They consist in reducing integral equations to simpler equations and systems, for example, systems of linear algebraic equations, and further solving these simpler equations. Methods of presenting the initial data of integral models in the MATLAB system are described, which involve two ways of describing the initial structures: in tabular and analytical form. Methods of data verification in the MATLAB environment are described, which allows you to ensure the predicted behavior of modules and avoid unforeseen situations. The solutions and recommendations for the construction of functions in the MATLAB system proposed in the work were used in the construction of tools for the study of integral models in the form of Volterra integral equations. On the example of the implementation of quadrature and collocation methods for solving integral equations, the peculiarities of the organization of program modules in the programming language built into the MATLAB system are shown. The developed tools are characterized by maximum use of matrix-vector calculations, optimal use of memory, and safe verification and processing of data correctness.