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1
Content available A new modification of the reduced differential transform method for nonlinear fractional partial differential equations
Khalouta Ali, Kadem Abdelouahab
Journal of Applied Mathematics and Computational Mechanics
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2020
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Vol. 19, nr 3
45--58
EN
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.
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 A study on magneto hydrodynamics Jeffery-Hamel flow with heat transfer problem in Eyring-Powell fluid using differential transform method
Meher Ramakanta, Patel N. D.
Journal of Applied Mathematics and Computational Mechanics
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2019
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Vol. 18, nr 3
57--68
EN
In this paper, we study and analyse the variations of velocity profiles for different values of the Reynolds number, Eckert number, Prandtl number and Hartmann number in the Magneto Hydrodynamics Jeffery-Hamel flow with heat transfer in Eyring-Powell fluid in both divergent and convergent channels. The Differential Transform Method (DTM) is used to obtain an analytical solution of the Jeffery Hamel flow problem and to determine the velocity profiles of the fluid flow. Finally, the efficiency of DTM has been shown, and the results have been validated by comparing the obtained results with the numerical results (fourth order RK method) in both convergent and divergent channels.
4
Content available Investigation of a Jeffery-Hamel flow between two rectangular inclined smooth walls using the differential Transform Method
Patel N. D., Meher R.
Journal of Applied Mathematics and Computational Mechanics
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2018
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Vol. 17, nr 4
47--57
EN
In this article, the Differential Transform Method (DTM) is applied to derive a semi-analytic solution for the non-linear MHD (Magneto Hydro Dynamics) Jeffery-Hamel flow between rectangular inclined smooth planes. A non-linear ordinary differential equation of order four is obtained from Navier-Stokes equations using similar transformation. A comparison between DTM, PM (Perturbation Method) and numerical solution is shown here to validate the obtained results with its convergence analysis for different values of m and a Reynolds number in divergent channels.
5
Content available Mixed convective fully developed flow in a vertical channel in the presence of thermal radiation and viscous dissipation
Prasad K. V., Mallikarjun P., Vaidya H.
International Journal of Applied Mechanics and Engineering
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2017
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Vol. 22, no. 1
123--144
EN
The effect of thermal radiation and viscous dissipation on a combined free and forced convective flow in a vertical channel is investigated for a fully developed flow regime. Boussinesq and Roseseland approximations are considered in the modeling of the conduction radiation heat transfer with thermal boundary conditions (isothermal-thermal, isoflux-thermal, and isothermal-flux). The coupled nonlinear governing equations are also solved analytically using the Differential Transform Method (DTM) and regular perturbation method (PM). The results are analyzed graphically for various governing parameters such as the mixed convection parameter, radiation parameter, Brinkman number and perturbation parameter for equal and different wall temperatures. It is found that the viscous dissipation enhances the flow reversal in the case of a downward flow while it counters the flow in the case of an upward flow. A comparison of the Differential Transform Method (DTM) and regular perturbation method (PM) methods shows the versatility of the Differential Transform Method (DTM). The skin friction and the wall temperature gradient are presented for different values of the physical parameters and the salient features are analyzed.
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