ABOUT WAVELET-BASED MULTIGRID NUMERICAL METHOD OF STRUCTURAL ANALYSIS WITH THE USE OF DISCRETE HAAR BASIS

he distinctive paper is devoted to so-called multigrid (particularly two-grid) method of structural analysis based on discrete Haar basis (one-dimensional, two-dimensional and three-dimensional problems are under consideration). Approximations of the mesh functions in discrete Haar bases of zero and first levels are described (the mesh function is represented as the sum in which one term is its approximation of the first level, and the second term is so-called complement (up to the initial state) on the grid of the first level). Special projectors are constructed for the spaces of vector functions of the original grid to the space of their approximation on the first-level grid and its complement (the refinement component) to the initial state. Basic scheme of the two-grid method is presented. This method allows solution of boundary problems of structural mechanics with the use of matrix operators of significantly smaller dimension. It should be noted that discrete analogue of the initial operator equation is a system of linear algebraic equations which is constructed with the use of finite element method or finite difference method. Block Gauss method can be used for direct solution

Combined variational iteration method with chebyshev wavelet for the solution of convection-diffusion-reaction problem

The goal of the work is to solve the nonlinear convection-diffusion-reaction problem using the variational iteration method with the combination of the Chebyshev wavelet. This work developed a hybrid iterative technique named as Variational iteration method with the Chebyshev wavelet for the solutions of nonlinear convection-diffusion-reaction problems. The aim of applying the derived algorithm is to achieve fast convergence. During the solution of the given problem, the restricted variations will be mathematically justified. The effects of the scaling and other parameters like diffusion parameter, convection parameter, and reaction parameter on the solution are also focused on by their suitable selection. The approximate results include the error profiles and the simulations. The results of variational iteration with the Chebyshev wavelet are compared with variational iteration method, the Modified variational iteration method, and the Variational iteration method with Legendre wavelet. The error profiles allow us to compare the results with well-known existing schemes

Fractional Calculus - Theory and Applications

In recent years, fractional calculus has led to tremendous progress in various areas of science and mathematics. New definitions of fractional derivatives and integrals have been uncovered, extending their classical definitions in various ways. Moreover, rigorous analysis of the functional properties of these new definitions has been an active area of research in mathematical analysis. Systems considering differential equations with fractional-order operators have been investigated thoroughly from analytical and numerical points of view, and potential applications have been proposed for use in sciences and in technology. The purpose of this Special Issue is to serve as a specialized forum for the dissemination of recent progress in the theory of fractional calculus and its potential applications

Modelación físico-matemática para la toma de decisiones frente a la COVID-19 en Cuba

Objective: To apply physico-mathematical modeling to the dynamics of COVID-19 that enables decision-making associated with mitigation and eradication of the pandemics in Cuba. Methods: Modeling was applied in order to characterize the predicted peak timing, and the reproductive performance of the pandemic, through MATLAB tools and functions. Peak timing was determined with the application of the SIR model, after adjustments. It was fit using the GlobalSearch optimization strategy. Function ode23tb was used in the solution, including a Runge-Kutta algorithm combined with another trapezoidal rule algorithm. To determine reproductive performance, an exponential model was fit using Curve Fitting. Main results: The parameters of the SIR model were identified, and the peak forecast was completed rapidly and accurately, two weeks before it occurred. The susceptible, accumulated infected and recovered patients were predicted. The calculated basic reproduction number (R0) helped conclude that to eradicate the pandemic by vaccination, the immunized population should be over 72 %. The effective reproduction number (Ref) helped evaluate the efficacy of mitigation measures. Remarks are made concerning the proper conduct to follow for eradication. Conclusions: The SIR model proved its capacity to predict the peak timing of the pandemic. The R0 of SARS-CoV-2 corroborated the high transmissibility of the virus. The mitigation measures have been effective, and should be kept until the pandemic is eradicated, even with Ref < 1, until 72 % of the population is immunized.Objetivo: Aplicar la modelación físico-matemática a la dinámica de la COVID-19 para la toma de decisiones asociadas a la mitigación y erradicación de la pandemia en Cuba. Métodos: La modelación se aplicó para caracterizar el pronóstico del pico y el comportamiento reproductivo de la pandemia, mediante herramientas y funciones de MATLAB. El pico se determinó aplicando el modelo SIR, luego de adecuaciones. Este se ajustó con la estrategia de optimización GlobalSearch. Para su solución se empleó la función ode23tb que usa un algoritmo combinado de Runge-Kutta con otro de regla trapezoidal. Para el comportamiento reproductivo se realizó el ajuste de un modelo exponencial empleando la herramienta Curve Fitting. Principales resultados: Se identificaron los parámetros del modelo SIR y se logró el pronóstico del pico con dos semanas de anticipación y una precisión satisfactoria. Se pronosticaron los susceptibles, infectados acumulados y recuperados. El número de reproducción básico (R0) calculado permitió determinar que, para erradicar la pandemia por vacunación, la población inmunizada debe ser superior al 72 %. El número de reproducción efectivo (Ref) permitió evaluar la eficacia de las medidas de mitigación. Se reflexionó sobre la conducta a seguir para su erradicación. Conclusiones: El modelo SIR demostró capacidad para predecir el pico de la pandemia. El R0 del SARS-CoV-2 permitió corroborar su elevada transmisibilidad. Las medidas de mitigación han sido efectivas y deben mantenerse hasta erradicar la pandemia, incluso para Ref < 1, mientras no se inmunice el 72 % de la población, para lograr la erradicación irreversible

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described