A comparison between the Differential Transform Method and the Adomian Decomposition Method for the Burgers equation
Journal Title: International Journal of engineering Research and Applications - Year 2017, Vol 7, Issue 12
Abstract
In this paper, we consider the Differential Transform Method (DTM)and the Adomian Decomposition Method (ADM) for finding approximate and exact solution of the Burgers equation. Moreover, the reliability and performance of DTM and ADM. Numerical results show that these methods are powerful tools for solving Burgers equation. A simple model of turbulence is represented by Burgerβs equation ππ’ ππ‘ + π’ ππ’ ππ₯ = π π 2π’ ππ₯ 2 , π < π₯ < π , π‘ > 0 1 With the initial condition π’ π₯, 0 = π π₯ , π < π₯ < π 2 and the boundary conditions: π’ π,π‘ = π1 π‘ , π’ π,π‘ = π2 π‘ , π‘ > 0 3 where π is the kinematic viscosity. Thus Burgerβs equation is as balance between time evolution, nonlinearity and diffusion. It may be noted that the equation is parabolic if π β 0 and hyperbolic if π = 0.
Authors and Affiliations
Ahmad M. D. Al- Eybani
Keywords
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