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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]

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]

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]

The model is a system of two nonlinear ordinary differential equations (ODEs) with dependent variables: the number of bees working in the hive and the number of bees that work outside the hive referred here as foragers. The population dynamics is studied. In this small study we present an effective simple algorithm to solve the parameter identification problem of the model in [10]. The parameters are identified using a least square method combined with backward Euler approximation of the ODE system and a Newton method technique for optimization of the cost functional. Numerical results of the parameters, representing the solution to the inverse problem are provided. [ABSTRACT FROM AUTHOR]

Inverse, or coefficient identification problem for honey bee colony population model is considered. On the base of the numerical solution to a weakly coupled system of ordinary differential equations (ODEs) with initial conditions, specific constant parameters are found by minimization of a quadratic discrete functional, which expresses the difference between the computed and measured numbers of bees working in and outside the hive. The optimization procedure uses quasilinearization which assures second order of convergence. Numerical simulations with synthetic and real data are discussed. [ABSTRACT FROM AUTHOR]

We investigate a specific ill-posed nonlinear inverse problem that arise on the financial markets. Precisely, as a benchmark problem, we consider the simultaneous recovery of implied volatility and interest rate functions over a finite interval corresponding to call and put prices for idealized continuous European vanilla options over the same maturity. In order to find these time-dependent functions, we minimize the cost functional which is the sum of the squared error between the market values and the computed values, obtained by implicit difference scheme for the Black–Scholes model. Furthermore, results of numerical experiments are discussed. [ABSTRACT FROM AUTHOR]

The paper aims to develop an algorithm to solve the inverse problem of identifying the volatility with given point measurements in a regime-switching economy. This value is of a particular importance since it is one of the main ingredients forming the option premia. After a review on the existing results for the classical Black–Scholes framework (equivalent to one regime), the direct and the inverse problems considering two regimes are defined. The forward problem is solved by applying the Simpson’s rule to an existing exact formula, while the inverse problem is tackled using a root-finding algorithm, namely Levenberg–Marquardt. What is more, a closed-form approximation formula for computing the implied volatility is proposed when at-the-money case is assumed. The numerical performance of the algorithms is studied and they are compared with a FDS approach. The paper is closed with a discussion and final remarks outlining the usefulness and applicability of the results. [ABSTRACT FROM AUTHOR]

We study the numerical approximation of the implied volatility for models in option pricing that generalize the Black–Scholes equation when the processes which generate the underlying stock returns may contain both continuous part and jumps. Here we propose weighted positive difference schemes with implicit-explicit iterations to solve the integral terms explicitly. We aim to identify the volatility from extra point measurement. First, we linearize in time the diffusion quadratic nonlinear term. Next, we employ a special decomposition of the approximate solution. Numerical tests are presented to show the computational efficiency of the algorithms. [ABSTRACT FROM AUTHOR]

This paper is devoted to develop a robust numerical algorithm to solve inverse problems of determining the right boundary conditions according to measurements inside a truncated domain for regime-switching models of European options. Difference schemes on Tavella-Randall grids are derived. We propose and discuss results of computational experiments for a several European options. [ABSTRACT FROM AUTHOR]

This paper is devoted to develop a robust numerical algorithm to solve inverse problems of determining the right boundary conditions according to measurements inside a truncated domain for regime-switching models of European options. Difference schemes on Tavella-Randall grids are derived. We propose and discuss results of computational experiments for a several European options. [ABSTRACT FROM AUTHOR]

In this work we report the development of an algorithm to solve inverse problems of determining the right boundary condition according to a measurement inside a truncated domain for the Black-Scholes equation. The difference schemes for the direct and inverse problems are derived on non-uniform Tavella-Randall grids. We propose and discuss results of computational experiments for several European options. [ABSTRACT FROM AUTHOR]