A Solution of the Burger’s Equation Arising in the Longitudinal Dispersion Phenomenon in Fluid Flow through Porous Media by Mixture of New Integral Transform and Homotopy Perturbation Method

The main aim of the paper is to examine the concentration of the longitudinal dispersion phenomenon arising in fluid flow through porous media. These phenomenon yields a partial differential equation namely Burger’s equation, which is solved by mixture of the new integral transform and the homotopy perturbation method under suitable conditions and the standard assumption. This method provides an analytical approximation in a rapidly convergent sequence with in exclusive manner computed terms. Its rapid convergence shows that the method is trustworthy and introduces a significant improvement in solving nonlinear partial differential equations over existing methods. It is concluded that the behaviour of concentration in longitudinal dispersion phenomenon is decreases as distance x is increasing with fixed time t > 0 and slightly increases with time t.

The Mixture of New Integral Transform and Homotopy Perturbation Method for Solving Discontinued Problems Arising in Nanotechnology

In this paper, a reliable algorithm based on mixture of new integral transform and homotopy perturbation method is proposed to solve a nonlinear differential-difference equation arising in nanotechnology. Continuum hypothesis on nanoscales is invalid, and a differential-difference model is considered as an alternative approach to describing discontinued problems. The technique finds the solution without any discretization or restrictive assumptions and avoids the round-off errors. Comparison of the approximate solution with the exact one reveals that the method is very effective. It provides more realistic series solutions that converge very rapidly for nonlinear real physical problems.

Mathematical modeling of tsunami wave propagation at mid ocean and its amplification and run-up on shore

The paper deals with the study of the mathematical model of tsunami wave propagation along a coast-line of an ocean.The model is based on shallow-water assumption which is represented by a system of non-linear partial differential equations.In this study,we employ the Elzaki Adomian Decomposition Method(EADM)to successfully obtain the solution for the proposed model for different coastal slopes and ocean depths.How tsunami wave velocity and run-up height are affected by the coast slope and sea depth are demonstrated.The Adomian Decomposition Method together with Elzaki transform allows for solutions,without the need of any linearization or perturbation,in the form of rapidly converging series.The obtained numerical results for tsunami wave height and velocity are very close match to the real physical phenomenon of tsunami.

Mathematical modeling of atmospheric internal waves phenomenon and its solution by Elzaki Adomian decomposition method

This article involves the study of atmospheric internal waves phenomenon,also referred to as gravity waves.This phenomenon occurs inside the fluid,not on the surface.The model is based on a shallow fluid hypothesis represented by a system of nonlinear partial differential equations.The basic assumption of the shallow flow model is that the horizontal size is much larger than the vertical size.Atmospheric internal waves can be perfectly represented by this model as the waves are spread over a large horizontal area.Here we used the Elzaki Adomian Decomposition Method(EADM)to obtain the solution for the considered model along with its convergence analysis.The Adomian decomposition method together with the Elzaki transform gives the solution in a convergent series without any linearization or perturbation.Comparisons are built between the results obtained by EADM and HAM to examine the accuracy of the proposed method.