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1
Content available Analytical solution of the time fractional Fokker-Planck equation
Sutradhar T., Datta B. K., Bera R. K.
International Journal of Applied Mechanics and Engineering
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2014
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Vol. 19, no. 2
435--440
EN
A nonperturbative approximate analytic solution is derived for the time fractional Fokker-Planck (F-P) equation by using Adomian’s Decomposition Method (ADM). The solution is expressed in terms of Mittag-Leffler function. The present method performs extremely well in terms of accuracy, efficiency and simplicity.
2
Content available remote Nonperturbative analytical solution of the time fractional advection problem
Sutradhar T., Datta B. K., Bera R. K.
International Journal of Applied Mechanics and Engineering
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2012
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Vol. 17, no. 2
629-636
EN
A nonperturbative analytic solution is derived for the time fractional nonlinear advection problem by using Adomian's Decomposition Method (ADM). The solution is obtained in the form of a power series with easily computable coefficients. The present method performs extremely well in terms of accuracy, efficiency and simplicity.
3
Content available remote Analytic solution of time fractional nonlinear dynamic system by modified decomposition method
Sutradhar T., Datta B. K., Bera R. K.
International Journal of Applied Mechanics and Engineering
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2012
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Vol. 17, no. 4
1327-1337
EN
Analytical and numerical results are reported for an analytical approximate solution of a nonlinear dynamic system containing fractional derivative by a modified decomposition method. Comparison with the exact and numerical solution shows that the present method performs extremely well in terms of accuracy, efficiency and simplicity.
4
Content available remote Solution of non-linear Klein-Gordan equation with a quadratic non-linear term by adomian decomposition method
Basak K. Ch., Ray P. Ch., Bera R. K.
International Journal of Applied Mechanics and Engineering
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2009
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Vol. 14, no 3
891-897
EN
Nonlinear PDEs are systematically solved by the decomposition method of Adomian for general boundary conditions described by boundary operator equations. In the present case, the solution of the nonlinear Klein-Gordon equation has been considered as an illustration of the decomposition method of Adomian.
5
Content available remote Application of Adomian Decomposition Method and Variational Iteration Method for the solution of a fractional (arbitrary) order differential equation
Ray S. S., Bera R. K.
International Journal of Applied Mechanics and Engineering
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2009
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Vol. 14, no 4
1169-1173
EN
In this paper, the Adomian decomposition method (ADM) and variational iteration method (VIM) are implemented to obtain an approximate solution to a fractional differential equation with an arbitrary order […]. The two methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions to different types of differential equations. In these schemes, the solution takes the form of a convergent series with easily computable components. The approximate solution obtained using the VIM is exactly the same and in good agreement as that obtained by using the ADM.
6
Content available remote Waves in thermoelastic materials with memory in generalized thermoelasticity
Baksi A., Bera R. K.
International Journal of Applied Mechanics and Engineering
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2006
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Vol. 11, no 4
771-785
EN
Many studies on classical thermoelastoicity have been denoted to materials with memory Nunziato, Chen and Gurtin, whereas few on generalized thermoelasticity address materials with memory. The present paper deals with the wave propagation in materials with memory in generalized thermoelasticity. Plane progressive waves and Rayleigh waves have been discussed in detail. The results show appreciable differences with those in the usual classical thermoelasticity theory.
7
Content available remote Application of Adomian method on the solution of wave propagation in a linear random non-homogeneous viscoelastic semi-infinite rod
Ray S. S., Bera R. K.
International Journal of Applied Mechanics and Engineering
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2005
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Vol. 10, no 1
133-143
EN
The aim of the present problem is to investigate the efficiency of the method of Adomian for the solution of non-linear and complicated differential equation in a random medium. Here the problem is connected with the investigation of the mean and variance of the displacement distribution in a thin linear random non-homogeneous Biot type viscoelastic semi-infinite rod, due to general time-dependent displacement input at the rod. A truncated series solution of the wave problem following the method of Adomian after using the Laplace transform is obtained for small random variations in viscoelastic properties. Three specific cases concerning the probability measure as a function of the continuous type of random variable have been discussed.
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