The approximation of an isolated epidemic process wave using a combination of exponents

The most commonly used methods for the medium- and long-term forecasting of epidemic processes are based on the classical SIR (susceptible – infected – recovered) model and its numerous modifications. In this approach, the dynamics of the epidemic is approximated using the solutions of differential or discrete equations. The forecasting methods based on the approximation of data by functions of a given class are usually focused on obtaining a short-term forecast. They are not used for the long-term forecasts of epidemic processes due to their insufficient efficiency for forecasting nonstationary processes. In this paper, we formulated a hypothesis that the primary waves of the COVID-19 pandemic, which took place in a number of European countries, including the Republic of Belarus, in the spring-summer of 2020 are isolated and therefore can be regarded as processes close to stationary. On the basis of this hypothesis, a method of approximating isolated epidemic process waves by means of generalized logistic functions with an increased number of exponents was proposed. The developed approach was applied to predict the number of infected people in the Republic of Belarus for the period until August 2020 based on data from the beginning of the epidemic until June 12, 2020.

Note on theoretical and practical solvability of a class of discrete equations generalizing the hyperbolic-cotangent class

There has been some recent interest in investigating the hyperbolic-cotangent types of difference equations and systems of difference equations. Among other things their solvability has been studied. We show that there is a class of theoretically solvable difference equations generalizing the hyperbolic-cotangent one. Our analysis shows a bit unexpected fact, namely that the solvability of the class is based on some algebraic relations, not closely related to some trigonometric ones, which enable us to solve them in an elegant way. Some examples of the difference equations belonging to the class which are practically solvable are presented, as well as some interesting comments on connections of the equations with some iteration processes.

Novel Hybrid Interval Type-2 Fuzzy Adaptive Backstepping Control for a Class of Uncertain Discrete-Time Nonlinear Systems

A Novel hybrid backstepping interval type-2fuzzy adaptive control (HBT2AC) for uncertain discrete-time nonlinear systems is presented in this paper. The systems are assumed to be defined with the aid of discrete equations with nonlinear uncertainties which are considered as modeling errors and external unknown disturbances, and that the observed states are considered disturbed. The adaptive fuzzy type-2 controller is designed, where the fuzzy inference approach based on extended single-input rule modules (SIRMs) approximate the modeling errors, non-measurable states and adjustable parameters are estimated using derived weighted simplified least squares estimators (WSLS). We can prove that the states are bounded and the estimation errors stand in the neighborhood of zero. The efficiency of the approach is proved by simulation for which the root mean squares criteria are used which improves control performance.

A Dimension Splitting Generalized Interpolating Element-Free Galerkin Method for the Singularly Perturbed Steady Convection–Diffusion–Reaction Problems

By introducing the dimension splitting method (DSM) into the generalized element-free Galerkin (GEFG) method, a dimension splitting generalized interpolating element-free Galerkin (DS-GIEFG) method is presented for analyzing the numerical solutions of the singularly perturbed steady convection–diffusion–reaction (CDR) problems. In the DS-GIEFG method, the DSM is used to divide the two-dimensional CDR problem into a series of lower-dimensional problems. The GEFG and the improved interpolated moving least squares (IIMLS) methods are used to obtain the discrete equations on the subdivision plane. Finally, the IIMLS method is applied to assemble the discrete equations of the entire problem. Some examples are solved to verify the effectiveness of the DS-GIEFG method. The numerical results show that the numerical solution converges to the analytical solution with the decrease in node spacing, and the DS-GIEFG method has high computational efficiency and accuracy.

A Hybrid Reproducing Kernel Particle Method for Three-Dimensional Advection-Diffusion Problems

In this paper, a hybrid reproducing kernel particle method (HRKPM) for three-dimensional (3D) advection-diffusion problems is presented. The governing equation of the advection-diffusion problem includes the second derivative of the field function to space coordinates, the first derivative of the field function to space coordinates and time, so it is necessary to discretize the time domain after discretizing the space domain. By introducing the idea of dimension splitting, a 3D advection-diffusion problem can be transformed into a series of related two-dimensional (2D) ones in the dimension splitting direction. Then, the discrete equations of these 2D problems are established by using the RKPM, and these discrete equations are coupled by using the difference method. Finally, by using the difference method to discretize the time domain, the formula of the HRKPM for solving 3D advection-diffusion problem is obtained. Numerical results show that the HRKPM has higher computational efficiency than the RKPM when solving 3D advection-diffusion problems.

A Dimension Splitting-Interpolating Moving Least Squares (DS-IMLS) Method with Nonsingular Weight Functions

By introducing the dimension splitting method (DSM) into the improved interpolating moving least-squares (IMLS) method with nonsingular weight function, a dimension splitting–interpolating moving least squares (DS-IMLS) method is first proposed. Since the DSM can decompose the problem into a series of lower-dimensional problems, the DS-IMLS method can reduce the matrix dimension in calculating the shape function and reduce the computational complexity of the derivatives of the approximation function. The approximation function of the DS-IMLS method and its derivatives have high approximation accuracy. Then an improved interpolating element-free Galerkin (IEFG) method for the two-dimensional potential problems is established based on the DS-IMLS method. In the improved IEFG method, the DS-IMLS method and Galerkin weak form are used to obtain the discrete equations of the problem. Numerical examples show that the DS-IMLS and the improved IEFG methods have high accuracy.

Convection – Diffusion – Radiation Heat and Mass Transfer to a Sphere Accompanied by a Surface Exothermal Chemical Reaction

The steady-state, coupled heat and mass transfer from a fluid flow to a sphere accompanied by an exothermal catalytic chemical reaction on the surface of the sphere is analysed taking into consideration the effect of thermal radiation. The flow past the sphere is considered steady, laminar and incompressible. The radiative transfer is modeled by P0 and P1 approximations. The mathematical model equations were discretized by the finite difference method. The discrete equations were solved by the defect correction – multigrid method. The influence of thermal radiation on the sphere surface temperature, concentration and reaction rate was analysed for three parameter sets of the dimensionless reaction parameters. The numerical results show that only for very small values of the Prater number the effect of thermal radiation on the surface reaction is not significant.

Numerical Solution of Coupled Thermo-Elastic-Plastic Dynamic Problems

The article considers a numerical method for solving a two-dimensional coupled dynamic thermoplastic boundary value problem based on deformation theory of plasticity. Discrete equations are compiled by the finite-difference method in the form of explicit and implicit schemes. The solution of the explicit schemes is reduced to the recurrence relations regarding the components of displacement and temperature. Implicit schemes are efficiently solved using the elimination method for systems with a three diagonal matrix along the appropriate directions. In this case, the diagonal predominance of the transition matrices ensures the convergence of implicit difference schemes. The problem of a thermoplastic rectangle clamped from all sides under the action of an internal thermal field is solved numerically. The stress-strain state of a thermoplastic rectangle and the distribution of displacement and temperature over various sections and points in time have been investigated.