Temat: ordinary differential equations - Katalog OPAC zbiorów

Skocz do pozycji: 1.

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: 2.

Tytuł:: Laplace-Carson integral transform for exact solutions of non-integer order initial value problems with Caputo operator
Autorzy:: Kumar, Prem
Qureshi, Sania
Powiązania:: https://bibliotekanauki.pl/articles/122736.pdf
Data publikacji:: 2020
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: ordinary differential equations
Laplace transform
Riemann-Liouville integral
równanie różniczkowe zwyczajne
transformacja Laplace'a
całka Riemann-Liouville
Opis:: Finding the exact solution to dynamical systems in the field of mathematical modeling is extremely important and to achieve this goal, various integral transforms have been developed. In this research analysis, non-integer order ordinary differential equations are analytically solved via the Laplace-Carson integral transform technique, which is a technique that has not been previously employed to test the non-integer order differential systems. Firstly, it has proved that the Laplace-Carson transform for n-times repeated classical integrals can be computed by dividing the Laplace-Carson transform of the underlying function by n-th power of a real number p which later helped us to present a new result for getting the Laplace-Carson transform for d-derivative of a function under the Caputo operator. Some initial value problems based upon Caputo type fractional operator have been precisely solved using the results obtained thereof.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 1; 57-66
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:: Using Shehu integral transform to solve fractional order Caputo type initial value problems
Autorzy:: Qureshi, Sania
Kumar, Prem
Powiązania:: https://bibliotekanauki.pl/articles/122809.pdf
Data publikacji:: 2019
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: ordinary differential equations
Laplace transform
Riemann-Liouville integral
równanie różniczkowe zwyczajne
transformata Laplace'a
całka Riemann-Liouville
Opis:: In the present research analysis, linear fractional order ordinary differential equations with some defined condition (s) have been solved under the Caputo differential operator having order α > 0 via the Shehu integral transform technique. In this regard, we have presented the proof of finding the Shehu transform for a classical nth order integral of a piecewise continuous with an exponential nt h order function which leads towards devising a theorem to yield exact analytical solutions of the problems under investigation. Varying fractional types of problems are solved whose exact solutions can be compared with solutions obtained through existing transformation techniques including Laplace and Natural transforms.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2019, 18, 2; 75-83
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:: Laplace-Carson integral transform for exact solutions of non-integer order initial value problems with Caputo operator
Autorzy:: Kumar, Prem
Qureshi, Sania
Powiązania:: https://bibliotekanauki.pl/articles/1839810.pdf
Data publikacji:: 2020
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: ordinary differential equations
Laplace transform
Riemann-Liouville integral
równanie różniczkowe zwyczajne
transformacja Laplace'a
całka Riemann-Liouville
Opis:: Finding the exact solution to dynamical systems in the field of mathematical modeling is extremely important and to achieve this goal, various integral transforms have been developed. In this research analysis, non-integer order ordinary differential equations are analytically solved via the Laplace-Carson integral transform technique, which is a technique that has not been previously employed to test the non-integer order differential systems. Firstly, it has proved that the Laplace-Carson transform for n-times repeated classical integrals can be computed by dividing the Laplace-Carson transform of the underlying function by n-th power of a real number p which later helped us to present a new result for getting the Laplace-Carson transform for d-derivative of a function under the Caputo operator. Some initial value problems based upon Caputo type fractional operator have been precisely solved using the results obtained thereof.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 1; 57-66
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:: 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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