The Inverse Problem of Determining the Parameters of a Mathematical Model Linking GDP with National Debt

2020 ◽  
Vol 31 (1) ◽  
pp. 75-95
Author(s):  
V. I. Dmitriev ◽  
E. S. Kurkina
Keyword(s):  
Mathematical Model ◽  
Inverse Problem ◽  
National Debt

A Meshless Method for Solving the Mathematical Model Associated the Leakage Problem in Gas Pipeline

2014 ◽  
Vol 986-987 ◽  
pp. 1418-1421
Author(s):  
Jun Shan Li
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Partial Differential Equation ◽  
Inverse Problem ◽  
Basis Function ◽  
Meshless Method ◽  
Numerical Solutions ◽  
Basis Functions ◽  
Gas Pipeline ◽  
The Mathematical Model

In this paper, we propose a meshless method for solving the mathematical model concerning the leakage problem when the pressure is tested in the gas pipeline. The method of radial basis function (RBF) can be used for solving partial differential equation by writing the solution in the form of linear combination of radius basis functions, that is, when integrating the definite conditions, one can find the combination coefficients and then the numerical solution. The leak problem is a kind of inverse problem that is focused by many engineers or mathematical researchers. The strength of the leak can find easily by the additional conditions and the numerical solutions.

SENSITIVITY ANALYSIS AND IDENTIFIABILITY OF A MATHEMATICAL MODEL OF A CHEMICAL REACTION

2021 ◽  
pp. 14-18
Author(s):  
Л.Ф. Сафиуллина
Keyword(s):  
Mathematical Model ◽  
Inverse Problem ◽  
Sensitivity Analysis ◽  
Chemical Reaction ◽  
Reaction Model ◽  
Numerical Calculations ◽  
Specific Reaction ◽  
Uniqueness Of The Solution ◽  
The Mathematical Model ◽  
Kinetics Of

В статье рассмотрен вопрос идентифицируемости математической модели кинетики химической реакции. В процессе решения обратной задачи по оценке параметров модели, характеризующих процесс, нередко возникает вопрос неединственности решения. На примере конкретной реакции продемонстрирована необходимость проводить анализ идентифицируемости модели перед проведением численных расчетов по определению параметров модели химической реакции. The identifiability of the mathematical model of the kinetics of a chemical reaction is investigated in the article. In the process of solving the inverse problem of estimating the parameters of the model, the question arises of the non-uniqueness of the solution. On the example of a specific reaction, the need to analyze the identifiability of the model before carrying out numerical calculations to determine the parameters of the reaction model was demonstrated.

GENERATION OF SYMMETRICAL COLORED IMAGES VIA SOLUTION OF THE INVERSE PROBLEM OF CHEMICAL REACTIONS DISCRETE CHAOTIC DYNAMICS

2006 ◽  
Vol 16 (05) ◽  
pp. 1419-1434 ◽  
Author(s):  
V. GONTAR ◽  
O. GRECHKO
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Model ◽  
Inverse Problem ◽  
Mathematical Models ◽  
Chemical Reactions ◽  
Chaotic Dynamics ◽  
Two Dimensional

An automatic procedure for generating colored two-dimensional symmetrical images based on the chemical reactions discrete chaotic dynamics (CRDCD) is proposed. The inverse problem of derivation of symmetrical images from CRDCD mathematical models was formulated and solved using a special type of genetic algorithm. Different symmetrical images corresponding to the solutions of a CRDCD mathematical model for which the parameters were obtained automatically by the proposed method are presented.

scholarly journals О постановках обратных задач

2020 ◽  
pp. 203-206
Author(s):  
Yurii Menshikov
Keyword(s):  
Mathematical Model ◽  
Inverse Problem ◽  
Approximate Solution ◽  
Inverse Problems ◽  
Solution Algorithms ◽  
The Mathematical Model

Some possible options for the formulation of inverse problems are considered. The ultimate research goals in these cases determine the algorithms for the approximate solution of the inverse problem and allow one to correctly interpret these solutions. Two main statements of inverse problems considered: inverse problems of synthesis and inverse problems of measurement. It is shown that in inverse synthesis problems one should not take into account the error of the mathematical model. In addition, it is possible in these cases to synthesize approximate solution algorithms that do not have a regularizing property. Examples of practical problems considered.

A numerical algorithm for constructing an individual mathematical model of HIV dynamics at cellular level

2018 ◽  
Vol 26 (6) ◽  
pp. 859-873 ◽  
Author(s):  
H. Thomas Banks ◽  
Sergey I. Kabanikhin ◽  
Olga I. Krivorotko ◽  
Darya V. Yermolenko
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Inverse Problem ◽  
Cellular Level ◽  
Free Virus ◽  
Hiv Dynamics ◽  
Infection Parameters ◽  
Simulation Results ◽  
The Mathematical Model ◽  
Fixed Times

Abstract In this paper a problem of specifying HIV-infection parameters and immune response using additional measurements of the concentrations of the T-lymphocytes, the free virus and the immune effectors at fixed times for a mathematical model of HIV dynamics is investigated numerically. The problem of the parameter specifying of the mathematical model (an inverse problem) is reduced to a problem of minimizing an objective function describing the deviation of the simulation results from the experimental data. A genetic algorithm for solving the least squares function minimization problem is implemented and investigated. The results of a numerical solution of the inverse problem are analyzed.

scholarly journals Modification of the Quasilinearization Method for the Inverse Problem

2007 ◽  
Vol 2007 ◽  
pp. 1-18
Author(s):  
Lenka Celechovská-Kozáková
Keyword(s):  
Mathematical Model ◽  
Inverse Problem ◽  
Approximate Solution ◽  
Nonlinear System ◽  
Best Approximation ◽  
Human Liver ◽  
Convergent Sequence ◽  
Iteration Step ◽  
Quasilinearization Method ◽  
The Best Approximation

We propose a new modification of Bellman's quasilinearization method such that at any iteration step, it works with an approximate solution of the original nonlinear system and with new approximation of parametersα(k+1)which are close enough to the previous ones. As an output, this approach provides a construction of a convergent sequence of parameters where the limit is the best approximation of parameters of a given system. We apply this method to a mathematical model describing BSP-kinetics in the human liver.

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