On Source Identification Problem for Telegraph Differential Equations

2016 ◽  
pp. 39-50 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Fatma Çekiç
Keyword(s):  
Differential Equations ◽  
Source Identification ◽  
Identification Problem

Numerical solution of a source identification problem: Almost coercivity

2019 ◽  
Vol 27 (4) ◽  
pp. 457-468 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Abdullah Said Erdogan ◽  
Ali Ugur Sazaklioglu
Keyword(s):  
Numerical Solution ◽  
Source Identification ◽  
Identification Problem ◽  
Second Order ◽  
Numerical Results ◽  
Difference Schemes ◽  
Stability Estimates ◽  
Order Of Accuracy ◽  
Accuracy Difference ◽  
Coercive Stability

Abstract The present paper is devoted to the investigation of a source identification problem that describes the flow in capillaries in the case when an unknown pressure acts on the system. First and second order of accuracy difference schemes are presented for the numerical solution of this problem. Almost coercive stability estimates for these difference schemes are established. Additionally, some numerical results are provided by testing the proposed methods on an example.

scholarly journals Asymptotic method for solution of identification problem of the nonlinear dynamic systems

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 1025-1033 ◽  
Author(s):  
F.A. Aliev ◽  
N.A. Ismailov ◽  
A.A. Namazov ◽  
N.A. Safarova ◽  
M.F. Rajabov ◽  
...  
Keyword(s):  
Differential Equations ◽  
Small Parameter ◽  
Least Squares Method ◽  
Identification Problem ◽  
Euler Method ◽  
Vector Parameter ◽  
Constant Vector ◽  
Unknown Constant ◽  
Linear Differential ◽  
The Right

A dynamic system, when the motion of the object is described by the system of nonlinear ordinary differential equations, is considered. The right part of the system involves the phase coordinates as a unknown constant vector-parameter and a small number. The statistical data are taken from practice: the initial and final values of the object coordinates. Using the method of quasilinearization the given equation is reduced to the system of linear differential equations, where the coefficients of the coordinate and unknown parameter, also of the perturbations depend on a small parameter linearly. Then, by using the least-squares method the unknown constant vector-parameter is searched in the form of power series on a small parameter and for the coefficients of zero and the first orders the analytical formulas are given. The fundamental matrices both in a zero and in the first approach are constructed approximately, by means of the ordinary Euler method. On an example the determination of the coefficient of hydraulic resistance (CHR) in the lift in the oil extraction by gas lift method is illustrated, as the obtained results in the first approaching coincides with well-known results on order of 10-2.

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