Analytical Solutions of the Navier-Stokes Model by He’s Polynomials

Navier-Stokes models are of great usefulness in physics and applied sciences. In this paper, He’s polynomials approach is implemented for obtaining approximate and exact solutions of the Navier-Stokes model. These solutions are calculated in the form of series with easily computable components. This technique is showed to be very effective, efficient and reliable because it gives the exact solution of the solved problems with less computational work, without neglecting the level of accuracy. We therefore, recommend the extension and application of this novel method for solving problems arising in other aspect of applied sciences. Numerical computations, and graphics done in this work, are through Maple 18

Splitting Decomposition Homotopy Perturbation Method To Solve One -Dimensional Navier -Stokes Equation

We have proposed in this  research a new scheme to find analytical  approximating solutions for Navier-Stokes equation  of  one  dimension. The  new  methodology depends on combining  Adomian  decomposition  and Homotopy perturbation methods  with the splitting time scheme for differential operators . The new methodology is applied on two problems of  the test: The first has an exact solution  while  the other one has no  exact solution. The numerical results we  obtained  from solutions of two problems, have good convergent  and high  accuracy   in comparison with the two traditional Adomian  decomposition  and Homotopy  perturbationmethods .&nbsp

A New Computational Method Based on Integral Transform for Solving Linear and Nonlinear Fractional Systems

In this article, the Elzaki homotopy perturbation method is applied to solve fractional stiff systems. The Elzaki homotopy perturbation method (EHPM) is a combination of a modified Laplace integral transform called the Elzaki transform and the homotopy perturbation method. The proposed method is applied for some examples of linear and nonlinear fractional stiff systems. The results obtained by the current method were compared with the results obtained by the kernel Hilbert space KHSM method. The obtained result reveals that the Elzaki homotopy perturbation method is an effective and accurate technique to solve the systems of differential equations of fractional order