A numerical solution for the source identification telegraph problem with Neumann condition

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.

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The Numerical Solution of the Bitsadze-Samarskii Nonlocal Boundary Value Problems with the Dirichlet-Neumann Condition

Abstract and Applied Analysis ◽

10.1155/2012/730804 ◽

2012 ◽

Vol 2012 ◽

pp. 1-13 ◽

Cited By ~ 5

Author(s):

Allaberen Ashyralyev ◽

Elif Ozturk

Keyword(s):

Numerical Solution ◽

Boundary Value ◽

Nonlocal Boundary ◽

Difference Schemes ◽

Neumann Condition ◽

Nonlocal Boundary Value Problem ◽

Numerical Examples ◽

Gauss Elimination ◽

Accuracy Difference ◽

Gauss Elimination Method

We are interested in studying the stable difference schemes for the numerical solution of the nonlocal boundary value problem with the Dirichlet-Neumann condition for the multidimensional elliptic equation. The first and second orders of accuracy difference schemes are presented. A procedure of modified Gauss elimination method is used for solving these difference schemes for the two-dimensional elliptic differential equation. The method is illustrated by numerical examples.

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Numerical solution to the second order of accuracy difference scheme for the source identification elliptic-telegraph problem

10.1063/5.0040389 ◽

2021 ◽

Author(s):

Allaberen Ashyralyev ◽

Ahmad Al-Hammouri

Keyword(s):

Difference Scheme ◽

Numerical Solution ◽

Source Identification ◽

Second Order ◽

Order Of Accuracy ◽

Accuracy Difference

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Parabolic time dependent source identification problem with involution and Neumann condition

BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS ◽

10.31489/2021m2/5-15 ◽

2021 ◽

Vol 102 (2) ◽

pp. 5-15

Author(s):

A. Ashyralyev ◽

◽

A.S. Erdogan ◽

◽

...

Keyword(s):

Differential Equation ◽

Approximate Solution ◽

Parabolic Equation ◽

Source Identification ◽

Parabolic Problem ◽

Identification Problem ◽

Time Dependent ◽

Neumann Condition ◽

Stability Estimates ◽

Well Posedness

A time dependent source identification problem for parabolic equation with involution and Neumann condition is studied. The well-posedness theorem on the differential equation of the source identification parabolic problem is established. The stable difference scheme for the approximate solution of this problem and its stability estimates are presented. Numerical results are given.

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On the Numerical Solution of the Initial-Boundary Value Problem with Neumann Condition for the Wave Equation by the Use of the Laguerre Transform and Boundary Elements Method

Acta Mechanica et Automatica ◽

10.1515/ama-2016-0044 ◽

2016 ◽

Vol 10 (4) ◽

pp. 285-290 ◽

Cited By ~ 1

Author(s):

Svyatoslav Litynskyy ◽

Yuriy Muzychuk ◽

Anatoliy Muzychuk

Keyword(s):

Wave Equation ◽

Boundary Value Problem ◽

Numerical Solution ◽

Boundary Value ◽

Initial Boundary ◽

Initial Boundary Value Problem ◽

Neumann Condition ◽

Laguerre Transform ◽

Boundary Elements Method ◽

Initial Boundary Value

Abstract We consider a numerical solution of the initial-boundary value problem for the homogeneous wave equation with the Neumann condition using the retarded double layer potential. For solving an equivalent time-dependent integral equation we combine the Laguerre transform (LT) in the time domain with the boundary elements method. After LT we obtain a sequence of boundary integral equations with the same integral operator and functions in right-hand side which are determined recurrently. An error analysis for the numerical solution in accordance with the parameter of boundary discretization is performed. The proposed approach is demonstrated on the numerical solution of the model problem in unbounded three-dimensional spatial domain.

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