Search

In this paper an advanced stochastic approach based a lattice rule with improved generating vector has been obtained and studied. The Unified Danish Eulerian Model (UNI-DEM) is a key element in our investigation since it is one of the most advanced large-scale mathematical models that describes adequately all physical and chemical processes. The calculations are done in a large spatial domain, which covers completely the European region and the Mediterranean, for certain time period. What is more, it studies the transportation of a number of pollutants and all these make it a perfect case study. The paper compares the described lattice rule and demonstrates its superiority over the plain Monte Carlo approach and Fibonacci based lattice rule. The proposed approach is robust and computationally efficient in estimating multidimensional integrals and thus sensitivity indices, which is vital in scientific computing. [ABSTRACT FROM AUTHOR]

Many problems of contaminant transport in porous media are described by parabolic equations on unbounded domains and must be solved numerically. For computation of such kind of problems, it is necessary to reduce them to a bounded domain and the question of appropriate boundary conditions arises. In this paper, using the Green function method (often called method of fundamental solutions), we propose a procedure for construction of efficient boundary conditions on arbitrary bounded domains for 1D and 2D parabolic Cauchy problems. The method is tested on a model of solute water pollution. [ABSTRACT FROM AUTHOR]

In the context of the COVID–19, a great deal of attention is attracted in studying the infectious disease from both academics and practitioners. One of the most powerful tools for simulating, analyzing and predicting the future epidemic development is the mathematical modelling. We adopted a fractional-order SEIR compartment model to investigate the disease underlying dynamics. The major aim of the present study is to propose an efficient algorithm to solve the coefficient identification inverse problem. The latter is formulated as a minimization problem for a quadratic cost functional, which is solved by a numerical optimization methods. The basic reproduction number and the economic impact of the epidemic are also discussed. Computational experiments with real-world data are provided to demonstrate the suggested algorithm properties. The paper is concluded with final remarks concerning the applicability of the approach and possible further research. [ABSTRACT FROM AUTHOR]

The recently observed honey bee colony losses have already raised concerns about the future of the managed honey bees and the bees in general. One of the most powerful approach to simulate and predict the dynamics of a complex system, which a honey bee colony undoubtedly is, is the mathematical modelling. We have adopted a compartment model to study the behaviour in a honey bee colony. A system of three ordinary differential equations with a control on the mites was introduced to model the populations of the hive bees, forager bees and mites. We solve a parameter identification inverse problem to reconstruct the values, which are directly unobservable but vital in honeybee management. We apply an adjoint equation optimization approach to solve the inverse problem. Numerical test examples are discussed and the paper is concluded with important implications about the honey bee management. [ABSTRACT FROM AUTHOR]

Financial markets and financial instruments and derivatives have experienced significant changes recently. Although this transition, the gold and crude oil are still leading the market and determine the main market conditions, so their importance could not be neglected. Looking back in history, there are milestone events that have drastically changed the economic, social and political circumstances, which have immediately affected the financial markets. In the recent study we calibrate jump-diffusion process to historical prices of gold (XAU) and crude brent oil futures (LCOc1), and derive piecewise approximations of the trend, volatility and jump intensity and distribution parameters. In the framework of jump-diffusion, we interpret the results as well as describe the possible future states of their prices and their impact on the global economy and quantify the respective outcomes probabilities. Based on the analysis, essential remarks for the economic environment are made in the conclusion of the paper. [ABSTRACT FROM AUTHOR]