Estimating the parameters of chemical kinetics equations from the partial information about their solution

Shatalov, M. Y.; Demidov, A. S.; Fedotov, Igor

doi:10.1134/s0040579516020111

Cited by 5 publications

(2 citation statements)

References 17 publications

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“…• Solution of the initial value problem (1) {x(t), y(t)} with positive initial conditions is positive, i.e. x(t) > 0 and y(t) > 0 for t ≥ 0.…”

Section: Resultsmentioning

confidence: 99%

“…The numerical evaluation of known coefficient of a dynamical system i.e. the problem of dynamical system identification, is one of the most important problem of the mathematical biology [1], ecology [2], [3], [4], etc. Usually, to identify a dynamics of a system, it is necessary to have certain statistical information for time values about the unknown functions of this system.…”

Section: Introductionmentioning

confidence: 99%

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Inverse problem of the Holling-Tanner model and its solution

Adeniji¹,

Fedotov²,

Shatalov³

2018

BIOMATH

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In this paper we undertake to consider the inverse problem of parameter identification of nonlinear system of ordinary differential equations for a specific case of complete information about solution of the Holling-Tanner model for finite number of points for the finite time interval. In this model the equations are nonlinearly dependent on the unknown parameters. By means of the proposed transformation the obtained equations become linearly dependent on new parameters functionally dependent on the original ones. This simplification is achieved by the fact that the new set of parameters becomes dependent and the corresponding constraint between the parameters is nonlinear. If the conventional approach based on introduction of the Lagrange multiplier is used this circumstance will result in a nonlinear system of equations. A novel algorithm of the problem solution is proposed in which only one nonlinear equation instead of the system of six nonlinear equations has to be solved. Differentiation and integration methods of the problem solution are implemented and it is shown that the integration method produces more accurate results and uses less number of points on the given time interval.

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“…• Solution of the initial value problem (1) {x(t), y(t)} with positive initial conditions is positive, i.e. x(t) > 0 and y(t) > 0 for t ≥ 0.…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%