Temat: równanie całkowe Fredholma - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: On approximate conformal mapping of a disk and an annulus with radial and circular slits onto multiply connected domains
Autorzy:: Ivanshin, Pyotr N.
Shirokova, Elena A.
Powiązania:: https://bibliotekanauki.pl/articles/1839828.pdf
Data publikacji:: 2020
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: conformal mapping
multiply connected domain
Fredholm integral equation
mapowanie konformalne
równanie całkowe Fredholma
domeny połączone
Opis:: The method of boundary curve reparametrization is generalized to the case of multiply connected domains. We construct the approximate analytical conformal mapping of the unit disk with m circular slits and n-m radial slits and an annulus with (m-1) circular slits and n-m radial slits onto an arbitrary given (n+1) multiply connected finite domain with a smooth boundary. The method is based on extension of the Lichtenstein-Gershgorin equation to a multiply connected domain. The proposed method is reduced to the solution of a linear system with unknown Fourier coefficients. The approximate mapping function has the form of a Cauchy integral. Numerical examples demonstrate that the proposed method is effective in computations.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 2; 73-84
2299-9965
Pojawia się w:: Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: Transformation of the second order boundary value problem into integral form : different approaches and a numerical solution
Autorzy:: Siedlecki, J.
Ciesielski, M.
Błaszczyk, T.
Powiązania:: https://bibliotekanauki.pl/articles/122740.pdf
Data publikacji:: 2015
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: BVP problem
Fredholm integral equation
Fubini's theorem
numerical methods
zagadnienie wartości brzegowych
równanie całkowe Fredholma
twierdzenie Fubinisa
metody numeryczne
Opis:: In this paper we present different approaches to the transformation of the second order ordinary differential equation, with respect to adequate boundary conditions, into integral equations. The obtained equations are Fredholm integral equations of the second kind. Next, a numerical method based on quadrature methods has been proposed to get an approximate solution of these equations.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2015, 14, 3; 103-108
2299-9965
Pojawia się w:: Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: Frictionless contact between a rigid indentor and a transversely isotropic functionally graded layer
Autorzy:: Patra, R.
Barik, S. P.
Chaudhuri, P. K.
Powiązania:: https://bibliotekanauki.pl/articles/947340.pdf
Data publikacji:: 2018
Wydawca:: Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:: równanie całkowe Fredholma
transformacja Hankela
rozkład naprężeń
functionally graded material
transversely isotropic medium
Hankel transform
contact problem
Fredholm integral equation
Opis:: This article is concerned with the study of frictionless contact between a rigid punch and a transversely isotropic functionally graded layer. The rigid punch is assumed to be axially symmetric and is supposed to be pressing the layer by an applied concentrated load. The layer is resting on a rigid base and is assumed to be sufficiently thick in comparison with the amount of indentation by the rigid punch. The graded layer is modeled as a non-homogeneous medium. The relationship between the applied load P and the contact area is obtained by solving the mathematically formulated problem through using the Hankel transform of different order. Numerical results have been presented to assess the effects of functional grading of the medium and the applied load on the stress distribution in the layer as well as on the relationship between the applied load and the area of contact.
Źródło:: International Journal of Applied Mechanics and Engineering; 2018, 23, 3; 655-671
1734-4492
2353-9003
Pojawia się w:: International Journal of Applied Mechanics and Engineering
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 4.

Tytuł:: Solving linear Fredholm integro-differential equation by Nyström method
Autorzy:: Tair, Boutheina
Guebbai, Hamza
Segni, Sami
Ghiat, Mourad
Powiązania:: https://bibliotekanauki.pl/articles/1839836.pdf
Data publikacji:: 2021
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: Fredholm integral equation
system of integral equations
integro-differential equations
Nyström method
równanie całkowe Fredholma
układ równań całkowych
równanie całkowo-różniczkowe
metoda Nyströma
Opis:: The study of the solution’s existence and uniqueness for the linear integro-differential Fredholm equation and the application of the Nyström method to approximate the solution is what we will present in this paper. We use the Neumann theorem to construct a sufficient condition that ensures the solution’s existence and uniqueness of our problem in the Banach space C1 [a,b]. We have applied the Nystrom method based on the trapezoidal ¨ rule to avoid adding other conditions in order to the approximation method’s convergence. The Nyström method discretizes the integro-differential equation into solving a linear system. Only with the existence and uniqueness condition, we show the solution’s existence and uniqueness of the linear system and the convergence of the numerical solution to the exact solution in infinite norm sense. We present two theorems to give a good estimate of the error. Also, to show the efficiency and accuracy of the Nyström method, some numerical examples will be provided at the end of this work.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2021, 20, 3; 53-64
2299-9965
Pojawia się w:: Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 5.

Tytuł:: Analytical and numerical study for a fractional boundary value problem with a conformable fractional derivative of Caputo and its fractional integral
Autorzy:: Bekkouche, M. Moumen
Guebbai, H.
Powiązania:: https://bibliotekanauki.pl/articles/1839786.pdf
Data publikacji:: 2020
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: fractional boundary value problem
Volterra-Fredholm integral equation
fractional derivative
fractional integral
równanie całkowe Volterry-Fredholma
ułamkowa wartość brzegowa
pochodna ułamkowa Caputo
Opis:: We study the existence and uniqueness of the solution of a fractional boundary value problem with conformable fractional derivation of the Caputo type, which increases the interest of this study. In order to study this problem we have introduced a new definition of fractional integral as an inverse of the conformable fractional derivative of Caputo, therefore, the proofs are based upon the reduction of the problem to a equivalent linear Volterra-Fredholm integral equations of the second kind, and we have built the minimum conditions to obtain the existence and uniqueness of this solution. The analytical study is followed by a complete numerical study.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 2; 31-42
2299-9965
Pojawia się w:: Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:: Biblioteka Nauki

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