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1
Content available A review: differential transform method for semi-analytical solution of differential equations
Rashidi M. M., Rabiei F., Naser Nia S., Abbasbandy S.
International Journal of Applied Mechanics and Engineering
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2020
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Vol. 25, no. 2
122--129
EN
In this article, the semi-analytical method known as the Differential Transform Method (DTM) for solving different types of differential equations is reviewed. First, basic definitions and formulas of DTM and Differential Transform-Padé approximation (DTM-Padé), which are used to increase the convergence and accuracy of DTM approximations, are discussed. Then both techniques of DTM and DTM-Padé, which have been successfully applied to partial differential equations, as well as the application of these methods in fluid mechanic and heat transfer are presented. In addition, the extension of DTM for integral differential equations and the fuzzy differential transformation method (FDTM) for fuzzy problems are discussed.
2
Content available The Generalized Differential Transform Method for solution of a free vibration linear differential equation with fractional derivative damping
Das Deepanjan
Journal of Applied Mathematics and Computational Mechanics
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2019
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Vol. 18, nr 2
19--29
EN
In the present paper, the Generalized Differential Transform Method (GDTM) is used for obtaining the approximate analytic solutions of a free vibration linear differential equation of a single-degree-of-freedom (SDOF) system with fractional derivative damping. The fractional derivatives are described in the Caputo sense.
3
Content available remote Integral equation of the Volterra type : an application to a firm-sponsored off-the-job training
Ekhosuehi V. U.
Mathematica Applicanda
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2016
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Vol. 44, No. 2
295--307
EN
This paper is concerned with deriving, using the Volterra integral equation, a production function for a single product firm financing off-the-job training from its revenue from output. The short-run scenario where labour is the only variable factor of production is studied within the the condition for profit-maximisation. The study utilises the Cobb-Douglas production function wherein capital is fixed as a theoretical underpinning. The Volterra integral equation is solved using the differential transform method. The solution reveals that the production function of the firm is a transcendental function. Some propositions on the properties of the new production function are stated along with their proofs. The behaviour of the production function is demonstrated by way of simulation.
PL
W artykule poszukuje się funkcji produkcji pojedynczego produktu w przedsiębiorstwie finansującym szkolenia ze środków uzyskanych ze sprzedaży tego produktu. Funkcja produkcji ma założoną formę równania całkowego Volterry a kryterium optymalizacji jest krótkoterminowa maksymalizacja zysku, w którym praca jest jedynym czynnikiem produkcji. W badaniu wykorzystano funkcję Cobba-Douglasa z ustaloną ilością kapitału. Wyniki wskazują, że otrzymana funkcja produkcji firmy jest funkcją analityczną, a wymagana część zysku potrzebna do sfinansowania szkolenia leży w przedziale z określoną górną granicą.
4
Content available Application of the differential transform method to the free vibration analysis of functionally graded timoshenko beams
Özdemir Ö.
Journal of Theoretical and Applied Mechanics
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2016
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Vol. 54 nr 4
1205--1217
EN
In this study, free vibration characteristics of a functionally graded Timoshenko beam that undergoes flapwise bending vibration is analysed. The energy expressions are derived by introducing several explanotary figures and tables. Applying Hamilton’s principle to the energy expressions, governing differential equations of motion and boundary conditions are obtained. In the solution part, the equations of motion, including the parameters for rotary inertia, shear deformation, power law index parameter and slenderness ratio are solved using an efficient mathematical technique, called the differential transform method (DTM). Natural frequencies are calculated and effects of several parameters are investigated.
5
Content available Application of the multi-step differential transform method to solve a fractional human T-cell lymphotropic virus I (HTLV-I) infection of CD4+ T-cells
Zurigat M., Ababneh M.
Journal of Mathematics and Applications
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2015
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Vol. 38
171--180
EN
Human T-cell Lymphotropic Virus I (HTLV-I) infection of CD4+ T-Cells is one of the causes of health problems and continues to be one of the significant health challenges. In this article, a multi-step differential transform method is implemented to give approximate solutions of fractional modle of HTLV-I infection of CD4+ T-cells. Numerical results are compared to those obtained by the fourth-order Runge-Kutta method in the case of intger-order derivatives. The suggested method is efficient as the Runge-Kutta method. Some plots are presented to show the reliability and simplicity of the method.
6
Content available remote A semi-analytical solution on static analysis of circular plate exposed to non-uniform axisymmetric transverse loading resting on Winkler elastic foundation
Abbasi S., Farhatnia F., Jazi S. R.
Archives of Civil and Mechanical Engineering
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2014
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Vol. 14, no. 3
476--488
EN
This paper is concerned with static analysis of functionally graded (FG) circular plates resting on Winkler elastic foundation. The material properties vary across the thickness direction so the power-law distribution is used to describe the constituent components. The differential transforms method (DTM) is utilized to solve the governing differential equations of bending of the thin circular plate under various boundary conditions. By employing this solution method, governing differential equations are transformed into recurrence relations and boundary/regularity conditions are changed into algebraic equations. In this study, the plate is subjected to uniform/non-uniform transverse load in two cases of boundary conditions (clamped and simply-supported). Some numerical examples are presented to show the influence of functionally graded variation, different elastic foundation modulus, and variation of the symmetrical transverse loads on the stress and displacement fields. Based on the results, the obtained out-plane displacement coincide with the available solution for a homogenous circular plate. It can be concluded that the applied method provides accurate results and it is easily used for static analysis of circular plates on an elastic foundation.
7
Content available Free vibration analysis of isotropic rectangular plates on Winkler foundation using differential transform method
Kumar Y.
International Journal of Applied Mechanics and Engineering
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2013
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Vol. 18, no. 2
589--597
EN
A differential transform method (DTM) is used to analyze free transverse vibrations of isotropic rectangular plates resting on a Winkler foundation. Two opposite edges of the plates are assumed to be simply supported. This semi-numerical-analytical technique converts the governing differential equation and boundary conditions into algebraic equations. Characteristic equations are obtained for three combinations of clamped, simply supported and free edge conditions on the other two edges, keeping one of them to be simply supported. Numerical results show the robustness and fast convergence of the method. Correctness of the results is shown by comparing with those obtained using other methods.
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