Verlan D. Methods and tools for numerical implementation of integral models of dynamic objects based on kernel separation

The thesis is devoted to development of mathematical and computer modeling of dynamic objects based on nonparametric dynamic models in the form of integral equations of Volterra and Fredholm, and to their numerical implementation through the design and application of efficient algorithms of kernel separation. In the thesis, the implementation of method of kernel separation for approximating functions of two variables is proposed for the first time. The method, unlike other (polynomial) methods, allows to get approximating bilinear series without previously choosing known system of coordinate functions, namely by pointwise determination of the functions in the process of approximation. It is implemented with 3 types of optimization algorithms - variational, variational-iterative and gradient. The method is characterized by high efficiency of the resulting approximating expression. Method of degenerate kernels for calculating the integral operators and solving Fredholm and Volterra integral equations of the first and the second kind was further developed. The method provides high performance of the computing process and creates the possibility of obtaining results in real time. First quadratic algorithms for solving Volterra and Fredholm linear integral equations of the first and the second kind that are based on computing and application of the resolvent used to derive explicit integral models of dynamic objects are designed. The algorithms are represented and implemented with a set of numerical arrays that are related to each other with corresponding computational operations.