Ivaniuk V. Methods and tools for mathematical modeling of dynamic processes in objects with distributed parameters based on the onedimensional integral models

The dissertation is devoted to the creation of methods and means for mathematical modeling dynamic processes in objects with distributed parameters in solving control and measurement problems based on one-dimensional integrated models. To reduce the complexity of algorithmic and software implementation of models and provide requirements for noise immunity and speed in control, monitoring and measurement systems, the following methods and tools have been developed: construction of simplified dynamic models in the form of one-dimensional integral operators and equations based on equivalent and approximate transformations of basic models by identifying them on the based on a series of experiments; numerical realization of one-dimensional polynomial Volterra integral operators based on the application of the vector-matrix approach and the method of separated kernels; solving inverse problems of dynamics for linear and nonlinear dynamical systems by applying regularization approaches to solving polynomial Volterra integral equations of the first kind. The developed tools and their effectiveness are illustrated by model examples and when solving applied problems.