Temat: derivative - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: A solution to the problem of time-fractional heat conduction in a multi-layer slab
Autorzy:: Siedlecka, U.
Kukla, S.
Powiązania:: https://bibliotekanauki.pl/articles/122925.pdf
Data publikacji:: 2015
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: heat conduction
fractional derivative
multi-layer slab
przewodnictwo ciepła
pochodna ułamkowa
Opis:: In this paper a solution of the time-fractional heat conduction problem in a multilayer slab is presented. The boundary conditions of the third kind and the perfect contact at the interfaces are assumed. A space-time dependent volumetric heat source in the slab and time dependent surroundings temperatures are taken into account in the formulation of the problem. The solution is obtained in the form of a series expansion with respect to eigenfunctions of an auxiliary problem. A numerical example shows temperature distribution in the slab for various values of the order of the Caputo fractional derivative in the heat conduction equation.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2015, 14, 3; 95-102
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:: Applying the topological derivative and the boundary element method to design of shape of the heat exchanger
Autorzy:: Freus, K.
Freus, S.
Powiązania:: https://bibliotekanauki.pl/articles/122334.pdf
Data publikacji:: 2015
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: topological derivative
topological sensitivity
Laplace equation
boundary element method
heat transfer
Opis:: In this work, the topological derivative for the Laplace equation is used to solve a design problem. This derivative describes the sensitivity of the problem when a small hole is formed at an arbitrary point of the domain. The goal of this work is to design topology of the domain when the Robin condition is imposed on the holes. Physically, the holes can be construed as cooling channels. For finding the solution of the governing equation the boundary element method is applied. The final part of the paper presents the design of the heat exchanger and results of computations.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2015, 14, 2; 5-12
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:: Time-fractional heat conduction in a finite composite cylinder with heat source
Autorzy:: Kukla, Stanisław
Siedlecka, Urszula
Powiązania:: https://bibliotekanauki.pl/articles/1839814.pdf
Data publikacji:: 2020
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: ractional heat conduction
Caputo derivative
composite cylinder
pochodna Caputo
cylinder kompozytowy
przewodzenie ciepła
Opis:: In this paper, the effect of the fractional order of the Caputo time-derivative occurring in heat conduction models on the temperature distribution in a finite cylinder consisting of an inner solid cylinder and an outer concentric layer is investigated. The inner cylinder (core) and the cylindrical layer are in perfect thermal contact. The Robin boundary condition on the outer surface and the Neumann conditions on the ends of the cylinder are assumed. An internal heat source is represented in the mathematical model by taking into account in the heat conduction equation of a function which depends on the space and time variable. An analytical solution of the problem is derived in the form of the double series of eigenfunctions. Numerical examples are presented.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 2; 85-94
2299-9965
Pojawia się w:: Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 4.

Tytuł:: Fractional heat conduction in multilayer spherical bodies
Autorzy:: Kukla, S.
Siedlecka, U.
Powiązania:: https://bibliotekanauki.pl/articles/122775.pdf
Data publikacji:: 2016
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: heat conduction
multilayer bodies
Caputo derivative
spherical coordinate
przewodnictwo cieplne
pochodna Caputo
współrzędna sferyczna
Opis:: In this paper an analytical solution of the time-fractional heat conduction problem in a spherical coordinate system is presented. The considerations deal the two-dimensional problem in multilayer spherical bodies including a hollow sphere, hemisphere and spherical wedge. The mathematical Robin conditions are assumed. The solution is a sum of time-dependent function satisfied homogenous boundary conditions and of a solution of the steady-state problem. Numerical example shows the temperature distributions in the hemisphere for various order of time-derivative.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2016, 15, 4; 83-92
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:: A new numerical technique for solving fractional Bratu’s initial value problems in the Caputo and Caputo-Fabrizio sense
Autorzy:: Khalouta, Ali
Kadem, Abdelouahab
Powiązania:: https://bibliotekanauki.pl/articles/1839797.pdf
Data publikacji:: 2020
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: fractional Bratu’s initial value problem
Caputo fractional derivative
Caputo-Fabrizio fractional derivative
natural transform method
Adomian decomposition method
ułamkowa pochodna Caputo
ułamkowa pochodna Caputo-Fabrizio
metoda transformacji naturalnej
metoda dekompozycji Adomiana
Opis:: The purpose of this paper is to propose a new numerical technique called the natural decomposition method (NDM) for solving fractional Bratu’s initial value problems (FBIVP) in the Caputo and Caputo-Fabrizio sense. The NDM is a combined form of the natural transform method and the Adomian decomposition method. The numerical example is provided in order to validate the efficiency and reliability of the proposed method. The obtained results reveal that the proposed method is a very efficient and simple tool for solving fractional differential equations.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 1; 43-56
2299-9965
Pojawia się w:: Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 6.

Tytuł:: A new numerical technique for solving fractional Bratu’s initial value problems in the Caputo and Caputo-Fabrizio sense
Autorzy:: Khalouta, Ali
Kadem, Abdelouahab
Powiązania:: https://bibliotekanauki.pl/articles/122619.pdf
Data publikacji:: 2020
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: fractional Bratu’s initial value problem
Caputo fractional derivative
Caputo-Fabrizio fractional derivative
natural transform method
Adomian decomposition method
ułamkowa pochodna Caputo
ułamkowa pochodna Caputo-Fabrizio
metoda transformacji naturalnej
metoda dekompozycji Adomiana
Opis:: The purpose of this paper is to propose a new numerical technique called the natural decomposition method (NDM) for solving fractional Bratu’s initial value problems (FBIVP) in the Caputo and Caputo-Fabrizio sense. The NDM is a combined form of the natural transform method and the Adomian decomposition method. The numerical example is provided in order to validate the efficiency and reliability of the proposed method. The obtained results reveal that the proposed method is a very efficient and simple tool for solving fractional differential equations.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 1; 43-56
2299-9965
Pojawia się w:: Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 7.

Tytuł:: Some differential operators in the symmetric bundle
Autorzy:: Kimaczyńska, A.
Powiązania:: https://bibliotekanauki.pl/articles/122502.pdf
Data publikacji:: 2017
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: symmetric tensors
symmetric derivative
gradient
divergence
Weitzenböck type formula
operator różnicowy
tensory symetryczne
pochodna symetryczna
Opis:: Some natural differential operators in the bundles of symmetric tensors and symmetric tensors with values in the tangent bundle are investigated. Applications in geometry, physics and tomography are also reviewed.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2017, 16, 3; 27-36
2299-9965
Pojawia się w:: Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 8.

Tytuł:: Numerical scheme for one phase 1D fractional Stefan problem using the similarity variable technique
Autorzy:: Błasik, M.
Powiązania:: https://bibliotekanauki.pl/articles/122307.pdf
Data publikacji:: 2014
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: Stefan problem
anomalous diffusion
fractional derivative
finite difference method
zagadnienie Stefana
dyfuzja anomalna
pochodna ułamkowa
metoda różnic skończonych
Opis:: In this paper we present a numerical method to solve a one-dimensional, one-phase extended Stefan problem with fractional time derivative described in the Caputo sense. The proposed method is based on applying a similarity variable for the anomalous-diffusion equation and the finite difference method. In the final part, examples of numerical results are discussed.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2014, 13, 1; 13-21
2299-9965
Pojawia się w:: Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 9.

Tytuł:: On the fractional-order dynamics of a double pendulum with a forcing constraint using the nonsingular fractional derivative approach
Autorzy:: Rangaig, Norodin A.
Pido, Alvanh Alem G.
Pada-Dulpina, Caironesa T.
Powiązania:: https://bibliotekanauki.pl/articles/1839787.pdf
Data publikacji:: 2020
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: fractional derivative
fractional Lagrangian
fractional Euler-Lagrange equation
double pendulum
pochodna ułamkowa
podwójne wahadło
równanie Eulera-Lagrange'a
Opis:: In this paper, we presented the fractional-order dynamics of a double pendulum, at a small oscillation, with a non-singular derivative kernel. The equation of motion has been derived from the fractional Lagrangian of the system and the considered fractional Euler-Lagrange equation. The generalized force has also been presented in studying the different cases of force, such as horizontal and vertical forcing. The source term is described by the imposed periodic force, and the memory effect gives an additional damping factor described by the fractional order. The integer and fractional orders of the sample phase diagrams were obtained and presented to visualize the effect of the presented fractional order on the system. Also, since the motion of the system dissipates in the fractional regime, the applied force will drive the system out of equilibrium.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 2; 95-106
2299-9965
Pojawia się w:: Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 10.

Tytuł:: Inexact Newton’s method for generalized operator equations in Banach spaces
Autorzy:: Singh, V. K.
Powiązania:: https://bibliotekanauki.pl/articles/122957.pdf
Data publikacji:: 2018
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: nonlinear operator equation
Fréchet derivative
Newton’s method
inexact
Newton method
pochodna Frécheta
metoda Newtona
niedokładna metoda Newtona
Opis:: In the present paper, we introduce a new inexact Newton-like algorithm for solving the generalized operator equations containing non differentiable operators in Banach space setting and discuss its semilocal convergence analysis under the weak Lipschitz condition with larger convergence domain and tighter error bounds. The main result of this paper is the significant improvement over the Newton’s method as well as the inexact Newton method.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2018, 17, 4; 85-97
2299-9965
Pojawia się w:: Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 11.

Tytuł:: A design of an optimal shape of domain described by NURBS curves using the topological derivative and boundary element method
Autorzy:: Freus, K.
Freus, S.
Powiązania:: https://bibliotekanauki.pl/articles/122807.pdf
Data publikacji:: 2017
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: Laplace equation
boundary element method
topological derivative
NURBS curves
równanie Laplace'a
metoda elementów brzegowych
pochodna topologiczna
krzywa NURBS
Opis:: The aim of this paper is to create an optimal shape of the 2D domain that is described by the Non-Uniform Rational B-Splines (NURBS) curves. This work presents a method based on the topological derivative for the Laplace equation that determines the sensitivity of a given cost function to the change of its topology. As a numerical approach, the boundary element method is considered. To check the effectiveness of the proposed approach, the example of computations was carried out.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2017, 16, 2; 67-76
2299-9965
Pojawia się w:: Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 12.

Tytuł:: Application of LDG scheme to solve semi-differential equations
Autorzy:: Izadi, Mohammad
Powiązania:: https://bibliotekanauki.pl/articles/122346.pdf
Data publikacji:: 2019
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: Caputo fractional derivative
local discontinuous Galerkin method
semi-differential equations
pochodna ułamkowa Caputo
nieciągła metoda Galerkina
schemat LDG
równania różnicowe
Opis:: In the current work, we investigate a technique based on discontinuous Galerkin method for the numerical approximation of semi-differential equations with Caputo’s fractional derivative. In this approach, using the natural upwind fluxes enables us to solve the model problem element by element locally in each subintervals and there is no need to solve a full global matrix. Numerical experiments are given to verify the efficiency and accuracy of the proposed method. Numerical solutions are compared with the exact solutions as well as the numerical solutions obtained by other available well-established computational procedures. The results show that the LDG method is more accurate for solving this class of differential equation with relatively low degrees of polynomials and number of elements.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2019, 18, 4; 27-39
2299-9965
Pojawia się w:: Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 13.

Tytuł:: Use of partial derivatives to derive a convergent numerical scheme with its error estimates
Autorzy:: Qureshi, Sania
Adeyeye, Oluwaseun
Shaikh, Asif Ali
Powiązania:: https://bibliotekanauki.pl/articles/122734.pdf
Data publikacji:: 2019
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: multi-derivative
local truncation error
stability
absolute relative errors
consistency
principal term
wielopochodna
pochodna cząstkowa
schemat numeryczny
błąd względny
błąd bezwzględny
Opis:: Using the idea of the partial derivative with respect to the ordinate of a given mathematical function, a new numerical scheme having third order convergence has been devised for solving initial value problems in ordinary differential equations. Such problems are deemed to be indispensable in diverse fields of science, medical and engineering and are most often required to be solved by the numerical schemes. In view of this, the proposed numerical scheme is found to be efficient in solving both autonomous and non-autonomous type of problems as supported by some numerical experiments in the present study. Using the Taylor expansion for the slopes involved in the scheme, the leading term of the local truncation error is shown to have contained Ϭ(h⁴) which proves third order accuracy of the scheme. In addition to this, consistency and linear stability analysis of the proposed scheme has extensively been discussed. Numerical experiments show better performance of the proposed numerical scheme when compared with existing numerical schemes of the same order as that of the scheme proposed. CPU time (seconds), maximum absolute relative error and the absolute relative error, computed at the last grid point of the integration interval for the associated initial value problem, are the parameters to test the performance of the proposed numerical scheme. MATLAB Version: 9.4.0.813654 (R2018a) in double-precision on a personal computer equipped with a Processor Intel (R) Core(TM) i3-4500U CPU@ 1.70 GHz running under the Windows 10 operating system has been employed in order to carry out all the required numerical computations.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2019, 18, 4; 73-83
2299-9965
Pojawia się w:: Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 14.

Tytuł:: New aspects on the fractional Euler-Lagrange equation with non-singular kernels
Autorzy:: Rangaig, Norodin A.
Powiązania:: https://bibliotekanauki.pl/articles/1839747.pdf
Data publikacji:: 2020
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: fractional derivative operator
non-singular kernel operator
fractional action-like integral
fractional Euler-Lagrange equation
operator pochodnej ułamkowej
równanie Eulera-Lagrange'a
Opis:: In this paper, we presented some notes in utilizing the fractional integral counterparts of the fractional derivatives with non-singular kernels on the action-like integral in Lagrangian mechanics. Considering a fractional integral, it may suggest that a dissipative term on the resulting fractional Euler-Lagrange equation can be obtained due to the imposed kernel. However, in the case of nonsingular kernel operators, different aspects of the fractional action-like integral were observed, and corresponding (fractionally-modified) Euler-Lagrange were derived, which imposes new insights on the dynamical system under the fractional regime.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 4; 89-100
2299-9965
Pojawia się w:: Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 15.

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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