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

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[1] Dmitriev V. I., Kurkina E. S. The inverse problem of determining the parameters of a mathematical model linking gdp with national debt // Computational Mathematics and Modeling. — 2020. — Vol. 30, no. 4. The article examines a mathematical model linking changes in GDP and in national debt. The model is based on a system of two linear ordinary differential equations (ODE) with variable coefficients. The model is approximate, but it describes the statistical data with good accuracy. The model coefficients are unknown. An algorithm is proposed to find the linear system coefficients from an approximate solution. A stable solution is obtained by the Tikhonov regularization method. Solving the forward and the inverse problem on prototype examples, we show that the time-dependent coefficients are reconstructed with good accuracy. The algorithm is applied to find and analyze the coefficients of a linear (ODE) system describing the dynamics of the national debt and GDP. The statistical data of several developed countries are applied to estimate the model coefficients and to analyze the dynamics of economic growth. [ DOI ]

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