DISCRETE AND CONTINUOUS MODELS AND APPLIED COMPUTATIONAL SCIENCE

A number of initial boundary-value problems of classical mathematical physics is generally represented in the linear operator equation and its well-posedness and causality in a Hilbert space setting was established. If a problem has a unique solution and the solution continuously depends on given data, then the problem is called well-posed. The independence of the future behavior of a solution until a certain time indicates the causality of the solution. In this article, we established the well-posedness and causality of the solution of the evolutionary problems with a perturbation, which is defined by a quadratic form. As an example, we considered the coupled system of the heat and Maxwell’s equations (the microwave heating problem).

In this article, we propose fourth- and fifth-order two-step iterative methods for solving the systems of nonlinear equations in

Various approaches to calculating normal modes of a closed waveguide are considered. A review of the literature was given, a comparison of the two formulations of this problem was made. It is shown that using a self-adjoint formulation of the problem of normal waveguide modes eliminates the occurrence of artifacts associated with the appearance of a small imaginary additive to the eigenvalues. The implementation of this approach for a rectangular waveguide with rectangular inserts in the Sage computer algebra system is presented and tested on hybrid modes of layered waveguides. The tests showed that our program copes well with calculating the points of the dispersion curve corresponding to the hybrid modes of the waveguide.

The paper considers a single-line retrial queueing system with an unreliable server. Queuing systems are called unreliable if their servers may fail from time to time and require restoration (repair), only after which they can resume servicing customers. The input of the system is a simple Poisson flow of customers. The service time and uptime of the server are distributed exponentially. An incoming customer try to get service. The server can be free, busy or under repair. The customer is serviced immediately if the server is free. If it is busy or under repair, the customer goes into orbit. And after a random time it tries to get service again. The study is carried out by the method of asymptotically diffusion analysis under the condition of a large delay of requests in orbit. In this work, the transfer coefficient and diffusion coefficient were found and a diffusion approximation was constructed.

Integrated Access and Backhaul (IAB) technology facilitates the establishment of a compact network by utilizing repeater nodes rather than fully equipped base stations, which subsequently minimizes the expenses associated with the transition towards next-generation networks. The majority of studies focusing on IAB networks rely on simulation tools and the creation of discrete-time models. This paper introduces a mathematical model for the boundary node in an IAB network functioning in half-duplex mode. The proposed model is structured as a polling service system with a dual-queue setup, represented as a random process in continuous time, and is examined through the lens of queueing theory, integral transforms, and generating functions (GF). As a result, analytical expressions were obtained for the GF, marginal distribution, as well as the mean and variance of the number of requests in the queues, which correspond to packets pending transmission by the relay node via access and backhaul channels.