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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 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]

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]

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]