# numerical simulation

## Semilinear periodic equation with arbitrary nonlinear growth and data measure: mathematical analysis and numerical simulation

In this work, we are interested in the existence, uniqueness, and numerical simulation of weak periodic solutions for some semilinear elliptic equations with data measures and with arbitrary growth of nonlinearities.  Since the data are not very regular and the growths are arbitrary, a new approach is needed to analyze these types of equations.  Finally, a suitable numerical discretization scheme is presented.  Several numerical examples are given which show the robustness of our algorithm.

## Tikhonov regularization for a spatiotemporal model of the human monkeypox outbreak

Monkeypox is a contagious disease caused by the monkeypox virus.  There is currently an outbreak of monkeypox in the U.S.

## A spatiotemporal spread of COVID-19 pandemic with vaccination optimal control strategy: A case study in Morocco

On March 2, 2020, the Moroccan Ministry of Health announced the first case of COVID-19 in the city of Casablanca for a Moroccan tourist who came from Italy.  The SARS-COV-2 virus has spread throughout the Kingdom of Morocco.  In this paper, we study the spatiotemporal transmission of the COVID-19 virus in the Kingdom of Morocco.  By supporting a SI$_{\rm W}$IHR partial differential equation for the spread of the COVID-19 pandemic in Morocco as a case study.  Our main goal is to characterize the optimum order of controlling the spread of the COVID-19 pandemic by adopting

## Study of two species prey–predator model in imprecise environment with harvesting scenario

This study proposes and explores a prey–predator model that presents a functional response to group behavior of prey–predator harvesting.  We study a non-linear model of prey–predator growths in two species.  The proposed model is supported by theoretical and numerical results.  Some numerical descriptions are provided to help our analytical and theoretical conclusions.  For all possible parameter values occurring in a prey–predator system, we solved it by using both VIM (variational iteration method) and HPM (homotopy perturbation method).  We also used MATLAB coding to compare our approxi

## Mathematical modeling and analysis of Phytoplankton–Zooplankton–Nanoparticle dynamics

In this paper, we investigate the population dynamics of phytoplankton–zooplankton–nanoparticle model with diffusion and density dependent death rate of predator.  The functional response of predator in this model is considered as Beddington–DeAngelis type.  The stability analysis of the equilibrium points is observed by applying the Routh–Hurwitz criterion.  Numerical simulations are given to illustrate the theoretical results.

## THEORETICAL ANALYSIS OF EXISTING CONCEPTS TO EVALUATE THE NON-FAILURE OF RC STRUCTURES IN OPERATION

The article presents a theoretical analysis of existing concepts to evaluate the non-failure of RC structures in operation. To perform the analysis, the authors considered a number of scientific works of both Ukrainian and foreign researchers. The main focus was on works in which the model of the stochastic nature of the RC structure operation included random parameters of acting loads, as well as the reserve of its bearing capacity and serviceability (geometric dimensions of cross sections of constructive members, strength and deformation characteristics of materials, etc.).

## Numerical exploration of mixed convection heat transfer features within a copper-water nanofluidic medium occupied a square geometrical cavity

The phenomenon of mixed convection heat transfer in a homogeneous mixture is deliberated thoroughly in this study for cooper-water nanofluids flowing inside a lid-driven square cavity.  By adopting the Oberbeck-Boussinesq approximation and using the single-phase nanofluid model, the governing partial differential equations modeling the present flow are stated mathematically based on the Navier--Stokes and thermal balance formulations, where the important features of the scrutinized medium are presumed to remain constant at the cold temperature.  Note here that the density quantity in the bu

## A modified adaptive large neighbourhood search for a vehicle routing problem with flexible time window

Vehicle routing problems are widely available in real world application.  In this paper, we tackle the resolution of a specific variant of the problem called in the literature vehicle routing problem with flexible time windows (VRPFlexTW), when the solution has to obey several other constraints, such as the consideration of travel, service, and waiting time together with time-window restrictions.  There are proposed two modified versions of the Multi-objective Adaptive Large Neighbourhood Search (MOALNS).  The MOALNS approach and its different components are described.

## Classical approach to determining the natural frequency of continual subsystem of three-mass inter-resonant vibratory machine

Problem statement. The three-mass vibratory system can be defined by five basic parameters: inertial parameters of the masses and stiffness parameters of two spring sets. Unlike the classical discrete system, the discrete-and-continual one consists of two rigid bodies connected by one spring set that form the discrete subsystem, and of the reactive mass considered as deformable (elastic) body characterized by certain stiffness and inertial parameters, which are related with one another.

## Determination of electrode spacings in laboratory tanks to obtain appropriate value of electric voltage

Purpose. The aim is to study the electrical potential distribution in dimensional limited and electrically insulated volume. Мethodology. It includes numerical simulation of stationary processes in Comsol 4.3а program using DC current’s module . Results. The numerical simulation was carried out for the area of electrically insulated tank. It length was L3 = 3[m] with depth of conducting medium H = 0.4[m]. The reference areas were L10 = 10[m] and L15 = 15[m] with the same depth as the regarded tank. The reference areas represents infinite medium with conductance about 200 [S].