Parameters identification of a distributed dynamical model using combined approach

Matveev, Mikhail; Kopytin, A.V.; Sirota, E. A.

doi:10.1088/1742-6596/1096/1/012068

Cited by 5 publications

(1 citation statement)

References 24 publications

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“…Moreover, in the present numerical computation, the result presented in Tables 1 and 2 shows that average absolute error (AAE), roots mean square error (𝐿 2 ) and pointwise maximum absolute error (𝐿 ∞ ) norms for the solution of example one are increasing as the number of mesh points 𝑀𝑥 and 𝑁𝑡 increases in both directions. But, the accuracy of the present methods is increasing, and it is superior to the accuracy of the method in [2,[25][26][27]. Fig.…”

Section: Discussionmentioning

confidence: 99%

Investigation the Accuracy of Crank Nicolson Methods and their Modified Schemes for One-Dimensional Linear Convection-Reaction-Diffusion Equations

Koroche

2024

AJOMCOR

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In this paper, Crank-Nicolson and Their Modified scheme are applied to find the solution of the convection-reaction-diffusion equation. First, the given solution domain is discretized. Then, using Taylor series expansion, we obtain the difference scheme of the model problem. By rearranging this scheme, we gain proposed techniques. To verify the validity of the proposed techniques, two model illustrations are considered. The stability and convergent analysis of the present scheme is worked by supporting the theoretical and numerical error bound. The accuracy of the present scheme has been shown in the sense of average absolute error, root means square error, and maximum absolute error norms. Then, the accuracy of the present techniques is compared with the accuracy obtained by another method in the literature. The physical behavior of the present results also has been shown in terms of graphs. As we can seen from the results in tables and physical behavior of solution, the present scheme approximates the exact solution veritably well. These scheme is improve the approximation exact solution of convection-reaction-diffusion equation. Hence, the present solution of convection-reaction-diffusion equation is accurate than pre-existing solution.

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Section: Discussionmentioning

confidence: 99%

Investigation the Accuracy of Crank Nicolson Methods and their Modified Schemes for One-Dimensional Linear Convection-Reaction-Diffusion Equations

Koroche

2024

AJOMCOR

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Dynamic identification of boundary conditions for convection-diffusion transport model subject to noisy measurements

Tsyganov

Tsyganova

Kuvshinova

2019

J. Phys.: Conf. Ser.

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The paper addresses the problem of dynamic identification of boundary conditions for one-dimensional convection-diffusion transport model based on noisy measurements of the function of interest. Using finite difference method the original model with the partial differential equation is replaced with the discrete linear dynamic system model with noisy multisensor measurements in which boundary conditions are included as the unknown input vector. To solve the problem, the algorithm of simultaneous the state and input vector estimation is used. The results of numerical experiments are presented which confirm the practical applicability of the proposed approach.

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Analysis of the properties of OLS-estimates in parameter identification of distributed dynamic processes

Matveev

Sirota

2020

J. Phys.: Conf. Ser.

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This work is devoted to analysis and research of OLS-estimates properties when identifying parameters of distributed dynamic processes. The study showed that at a low level of observation errors (1% and lower), the use of direct OLS estimates to identify parameters of distributed dynamic processes gives satisfactory results. At the same time, the displacement value is always slightly higher than the value of the standard deviation of the parameter estimate, which does not allow to neglect the displacement, especially at a high and average level of observation errors. The method of obtaining so-called alternative OLS-estimates is also proposed, which allows to reduce multicollinearity in sample statistics and at any level of observation errors significantly reduce standard error of parameter estimation.

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Parameters identification of a distributed dynamical model using combined approach

Cited by 5 publications

References 24 publications

Investigation the Accuracy of Crank Nicolson Methods and their Modified Schemes for One-Dimensional Linear Convection-Reaction-Diffusion Equations

Investigation the Accuracy of Crank Nicolson Methods and their Modified Schemes for One-Dimensional Linear Convection-Reaction-Diffusion Equations

Dynamic identification of boundary conditions for convection-diffusion transport model subject to noisy measurements

Analysis of the properties of OLS-estimates in parameter identification of distributed dynamic processes

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