Abstract
In this paper, we found the numerical solution of three-dimensional coupled Burgers’ Equations by using more efficient methods: Laplace Adomian decomposition method, Laplace transform homotopy perturbation method, variational iteration method, variational iteration decomposition method and variational iteration homotopy perturbation method. Example is examined to validate the efficiency and accuracy of these methods and they reduce the size of computation without the restrictive assumption to handle nonlinear terms and it gives the solutions rapidly.
Highlights
The Burgers Equation was first presented by Bateman [1] and treated later by J
We found the numerical solution of three-dimensional coupled Burgers’ Equations by using more efficient methods: Laplace Adomian decomposition method, Laplace transform homotopy perturbation method, variational iteration method, variational iteration decomposition method and variational iteration homotopy perturbation method
Burgers’ Equation is nonlinear partial differential equation of second order which is used in various fields of physical phenomena such as boundary layer behaviour, shock weave formation, turbulence, the weather problem, mass transport, traffic flow and acoustic transmission [3] [4]
Summary
The Burgers Equation was first presented by Bateman [1] and treated later by J. Coupled Burgers’ Equations has played an important role in many physical applications such as hydrodynamic turblence, vorticity transport, skock wave, dispersion in porous media and wave processes. The three-dimentional coupled Burgers’ Equations are important in large scale structure formation in the un-. Gave an numerical solution of one- and two-dimentional Burgers’ Equations [3] [8][15]. Shukla et al are proposed a numerical solutions of three-dimensional coupled viscous Burgers’ Equations by using a modified cubic B-spline differential quadrature method [5]. The motive of this paper is to find the numerical solution of three-dimensional coupled Burgers’ Equations by using more efficiently methods: Laplace Adomian decomposition method, Laplace transform homotopy perturbation method, the variational iteration method, variational iteration decomposition method and variational iteration homotopy perturbation method. It is clear to see that numerical methods are reasonably in good covenant with the exact solution
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