Temat: Nonlinear Equations - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Solving a system of nonlinear equations with the use of optimization methods in problems related to the wheel-rail contact
Autorzy:: Jureczko, M.
Duda, S.
Powiązania:: https://bibliotekanauki.pl/articles/122469.pdf
Data publikacji:: 2016
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: wheel-rail contact
system of nonlinear equations
Newton's method
trust region method
Levenberg-Marquardt method
damped Newton’s method
styk koło-szyna
układ równań nieliniowych
metoda Newtona
metoda Levenberg-Marquardt
Opis:: The article presents the methods for defining the geometry of the contact surface between a rigid wheel and a rigid rail. The calculation model that has been developed allowed for any arrangement of the wheel in relation to the rail. This allowed for the creation of a system of nonlinear equations, the solution of which allows one to determine the presumable wheel-rail contact points. The search for the solution of the system of strongly nonlinear equations was conducted using a few optimization methods. This allowed one to study both the selection of the starting point and the convergence of the method.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2016, 15, 2; 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: 2.

Tytuł:: Boundary integral solution for a class of fourth-order two-point boundary value problems
Autorzy:: Al-Gahtani, H. J.
Powiązania:: https://bibliotekanauki.pl/articles/122949.pdf
Data publikacji:: 2016
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: boundary integral method
fourth-order differential equation
nonlinear ordinary differential equations
nieliniowe równania różniczkowe zwyczajne
równanie różniczkowe czwartego rzędu
Opis:: In this paper, a boundary integral method is proposed for the solution of a class of fourth-order two-boundary value problems described by the equation y^iv+P(x, y, y^’, y^’’, y^’’’) = 0, x ∈ ( 0,L), where P is a polynomial function of its arguments. The differential equation is cast in an integral form and the weighted residual technique is used to generate the corresponding boundary integral equations. The boundary integral equations are then, solved by expressing the dependent variable, y, in terms of a power series. The proposed method is tested through four examples to show the applicability of the method to solve a wide range of fourth-order differential equations including the nonlinear ones.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2016, 15, 3; 5-13
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:: The homotopy analysis Rangaig transform method for nonlinear partial differential equations
Autorzy:: Ziane, Djelloul
Cherif, Mountassir Hamdi
Powiązania:: https://bibliotekanauki.pl/articles/2175522.pdf
Data publikacji:: 2022
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: Rangaig transform method
homotopy analysis method
nonlinear partial differential equations
metoda transformacji Rangaiga
metoda analizy homotopii
nieliniowe równania różniczkowe cząstkowe
Opis:: The idea suggested in this article is to combine the Rangaig transform with the homotopy analysis method in order to facilitate the solution of nonlinear partial differentia equations. This method may be called the homotopy analysis Rangaig transform method (HARTM). The proposed example results showed that HARTM is an effective method for solving nonlinear partial differential equations.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2022, 21, 2; 111--122
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:: Variation of parameters method for a three-dimensional problem of condensation film on an inclined rotating disk
Autorzy:: Güngör, Osman
Arslantürk, Cihat
Powiązania:: https://bibliotekanauki.pl/articles/122445.pdf
Data publikacji:: 2019
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: condensation
rotating inclined disk
nonlinear ordinary differential equations
variation of parameters method
VPM
kondensacja
nieliniowe równania różniczkowe zwyczajne
metoda zmiany parametrów
Opis:: In this paper, the steady three-dimensional problem of condensation film on an inclined rotating disk is considered. The governing nonlinear partial differential equations are reduced to the nonlinear ordinary differential equations system by a similarity transform. The equation system is solved by the variation of parameters method (VPM) which is rather used to solve nonhomogeneous linear differential equations but can also be used to solve nonlinear differential equations. This method has not previously been used to solve a nonlinear condensation problem. The dimensionless velocity and temperature profiles are shown, and the influence of Prandtl number and rotation ratio on the flow field and the Nusselt number are discussed in detail. In order to assess the accuracy of the solutions obtained by this method, the problem is also solved numerically using the Matlab bvp4c solver. The validity of our solutions is verified by the numerical results.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2019, 18, 1; 15-28
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 modification of the reduced differential transform method for nonlinear fractional partial differential equations
Autorzy:: Khalouta, Ali
Kadem, Abdelouahab
Powiązania:: https://bibliotekanauki.pl/articles/1839758.pdf
Data publikacji:: 2020
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: nonlinear fractional partial differential equations
Caputo fractional derivative
Shehu transform method
reduced differential transform method
approximate analytical solution
nieliniowe równania różniczkowe cząstkowe ułamkowe
pochodna ułamkowa Caputo
metoda transformacji Shehu
metoda transformacji różnicowej
Opis:: The objective of this study is to present a new modification of the reduced differential transform method (MRDTM) to find an approximate analytical solution of a certain class of nonlinear fractional partial differential equations in particular, nonlinear time-fractional wave-like equations with variable coefficients. This method is a combination of two different methods: the Shehu transform method and the reduced differential transform method. The advantage of the MRDTM is to find the solution without discretization, linearization or restrictive assumptions. Three different examples are presented to demonstrate the applicability and effectiveness of the MRDTM. The numerical results show that the proposed modification is very effective and simple for solving nonlinear fractional partial differential equations.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 3; 45-58
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:: Numerical study for a second order Fredholm integro-differential equation by applying Galerkin-Chebyshev-wavelets method
Autorzy:: Henka, Youcef
Lemita, Samir
Aissaoui, Mohamed-Zine
Powiązania:: https://bibliotekanauki.pl/articles/2202040.pdf
Data publikacji:: 2022
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: Fredholm integro-differential equations
nonlinear equation
Galerkin method
Chebyshev wavelets
równanie całkowo-różniczkowe Fredholma
równanie nieliniowe
metoda Galerkina
falki Czebyszewa
Opis:: In the present paper, we apply the Galerkin method using Chebyshev wavelets to approximate the exact solution for a second order Fredholm integro-differential equation with initial conditions. This numerical method gives us a nonlinear algebraic system that would be solved using the Picard successive approximations technique. Furthermore, we show the validity and the ability of the proposed method through some illustrative examples.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2022, 21, 4; 28--39
2299-9965
Pojawia się w:: Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:: Biblioteka Nauki

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