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1
Content available remote Numerical solution of heat diffusion equation using the generalized FDM
100%
Lara-Dziembek S. , Pawlak E.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2007
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tom Vol. 6, nr 1
117-125
EN
In the paper the numerical solution of boundary-initial problem described by the Fourier equation and adequate conditions is discussed. The algorithm bases on the concept of generalized finite difference method (GFDM). In the first part the mathematical formulation of the problem and a short description of GFDM algorithm are presented. In the second part the examples of numerical computations are shown. On the stage of computation the explicit version of GFDM is used.
2
Content available remote Identification of boundary heat flux using sequential and global function specification methods and FDM algorithm
100%
Lara-Dziembek S. , Pawlak E.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2011
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tom Vol. 10, nr 1
139-144
EN
In the paper the global function specification method is used for identification of the time dependent boundary heat flux on the external boundary of the domain considered. The additional information necessary to solve an inverse problem results from the knowledge of heating (cooling) curves at points selected from the interior of the domain. The mathematical model of thermal processes proceeding in the system is based on the Fourier equation. As an example, a 1D problem is considered, but generalization of the algorithm on 2D or 3D problems is not complicated. At the stage of the numerical solution of a direct problem and an additional one, the finite difference method has been applied.
3
Content available remote Weighted residual method as a tool of FDM algorithm construction
100%
Mochnacki B. , Lara-Dziembek S.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2010
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tom Vol. 9, nr 1
147-153
EN
Weighted Residual Method can be treated as a kind of "common root" of well known algorithms such as FDM, FEM, BEM, collocational methods etc. This point of view is completely motivated and it is possible to show that all of these methods are the special cases of WRM. In this paper the construction of typical FDM algorithm for non-linear parabolic equations (on the basis of WRM) is presented. To simplify the considerations, the 1D task is discussed.
4
Application of thermal and differential analysis in numerical solutions of inverse problems
100%
Szopa R. , Lara-Dziembek S.
Zeszyty Naukowe. Mechanika / Politechnika Opolska
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2009
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tom z. 95
87-88
5
Content available remote Curvilinear finite difference method (CFD) approximation of differential operators
100%
Lara-Dziembek S. , Siedlecki J.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2009
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tom Vol. 8, nr 1
97-103
EN
Curvilinear finite difference method is a one of variants of generalized finite difference method. Geometrical mesh can be created by the optional set of points for which the n-points stars are defined. In this paper the 9-points stars are considered (2D task) and the method of differential operators approximation is presented. In the final part of the paper the example of computations is shown.
6
Content available An example of non-Keller mapping
80%
Pawlak E. , Lara-Dziembek S. , Biernat G. , Woźniakowska M.
Journal of Applied Mathematics and Computational Mechanics
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2016
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tom Vol. 15, nr 1
115--121
EN
In the paper a nontrivial example of non-Keller mapping is considered. It is shown that the Jacobian of rare mapping, having one zero at infinity, being constant must vanish.
7
Content available remote The determinants of the block matrices in the 3D Fourier equation
80%
Biernat G. , Lara-Dziembek S. , Pawlak E.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2012
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tom Vol. 11, nr 4
5-10
EN
In the paper we present the method of calculating the determinant of the block matrix which characterizes internal heat conduction in the 3D case. The Finite Difference Method can be used.
8
Content available The n-dimensional Fourier equation with the Robin's boundary condition using the finite difference method
80%
Biernat G. , Lara-Dziembek S. , Pawlak E.
Journal of Applied Mathematics and Computational Mechanics
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2014
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tom Vol. 13, nr 3
13--20
EN
The article is a continuation of the considerations on the three-dimensional Fourier equation supplemented by the third boundary condition (the Robin’s condition). The paper is based on the Finite Difference Method.
9
Content available Symmetric polynomials in the 3D Fourier equation
80%
Biernat G. , Lara-Dziembek S. , Pawlak E.
Journal of Applied Mathematics and Computational Mechanics
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2015
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tom Vol. 14, nr 1
5--12
EN
The work is a continuation of the method of calculating the determinant of the block matrix in the three-dimensional case. In this article the symmetric polynomials are used.
10
Content available Some remarks to the Jacobian conjecture
80%
Lara-Dziembek S. , Biernat G. , Pawlak E.
Journal of Applied Mathematics and Computational Mechanics
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2017
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tom Vol. 16, nr 1
87--96
EN
This work is related to the Jacobian Conjecture. It contains the formulas concerning algebraic dependence of the polynomial mappings having two zeros at infinity and the constant Jacobian. These relations mean that such mappings are non-invertible. They reduce the Jacobian Conjecture only to the case of mappings having one zero at infinity. This case is already solved by Abhyankar. The formulas presented in the paper were illustrated by the large example.
11
Content available Symmetric polynomials in the 2D Fourier equation
80%
Biernat G. , Lara-Dziembek S. , Pawlak E.
Journal of Applied Mathematics and Computational Mechanics
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2014
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tom Vol. 13, nr 4
5--12
EN
The work is a continuation of the method of calculating the determinant of the block matrix in the two-dimensional case. In this paper we use the Finite Differences Method and the symmetric polynomials.
12
Content available The determinants of the block band matrices based on the n-dimensional Fourier equation
80%
Biernat G. , Lara-Dziembek S. , Pawlak E.
Journal of Applied Mathematics and Computational Mechanics
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2015
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tom Vol. 14, nr 3
5--15
EN
This paper contains the method of calculating the determinant of the block band matrix on the example of n-dimensional Fourier equation using the FDM.
13
Content available A second example of non-Keller mapping
80%
Lara-Dziembek S. , Biernat G. , Pawlak E. , Woźniakowska M.
Journal of Applied Mathematics and Computational Mechanics
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2016
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tom Vol. 15, nr 2
65--70
EN
In the article the next nontrivial example of non-Keller mapping having two zeros at infinity is analyzed. The rare mapping of two complex variables having two zeros at infinity is considered. In the article it has been proved that if the Jacobian of the considered mapping is constant, then it is zero.
14
Content available The finite difference method in the 2D Fourier equation with Robin’s boundary condition
80%
Biernat G. , Lara-Dziembek S. , Pawlak E.
Journal of Applied Mathematics and Computational Mechanics
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2013
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tom Vol. 12, nr 4
5--11
EN
This paper contains the application of the Finite Difference Method in the two-dimensional Fourier equation using Robin’s boundary condition (the third boundary condition).
15
Content available remote The determinants of the three-band block matrices
80%
Biernat G. , Lara-Dziembek S. , Pawlak E.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2012
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tom Vol. 11, nr 3
5-8
EN
In the paper the method of calculating of the determinants of block matrices is presented. The three-band matrices are considered, both in the particular case (3D) as well as in the general case.
16
Content available The Jacobians of non-maximal degree
80%
Lara-Dziembek S. , Biernat G. , Pawlak E.
Journal of Applied Mathematics and Computational Mechanics
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2016
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tom Vol. 15, nr 4
99--104
EN
In the article the leading forms of the polynomial mapping having the Jacobians of non-maximal degree are considered. In particular, the mappings having two zeros at infinity are discussed.
17
Content available The determinants of the block band matrices based on the n-dimensional Fourier equation. Part 1
80%
Biernat G. , Lara-Dziembek S. , Pawlak E.
Journal of Applied Mathematics and Computational Mechanics
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2013
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tom Vol. 12, nr 3
5--13
EN
This paper contains the method of calculating the determinant of the block band matrix on the example of n-dimensional Fourier equation using the Finite Difference Method.
18
Content available The 3D Fourier equation with the Robin’s boundary condition using the finite difference method
80%
Biernat G. , Lara-Dziembek S. , Pawlak E.
Journal of Applied Mathematics and Computational Mechanics
|
2014
|
tom Vol. 13, nr 1
5--11
EN
This article is a continuation of the discussion on the two-dimensional Fourier equation with Robin’s boundary condition. In the paper the Finite Difference Method is applied.
19
Content available The determinants of the block band matrices based on the n-dimensional Fourier equation. Part 2
80%
Biernat G. , Lara-Dziembek S. , Pawlak E.
Journal of Applied Mathematics and Computational Mechanics
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2013
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tom Vol. 12, nr 3
15--20
EN
This work is a continuation of the considerations concerning the determinants of the band block matrices on the example of the n-dimensional Fourier equation (work Part 1). The discussion will concern the special case called the three-dimensional Fourier equation.
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