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- Magdy A. El-Tawil, Ahmed A. Bahnasawi, Ahmed Abdel-Naby
- Applied Mathematics and Computation
- 2004

Adomian Decomposition method (ADM) is an approximate method, which can be adapted to solve nonlinear partial differential equations. In this paper, we solve the KdV and modified KdV (mKdV) equations using ADM-Padé technique, which gives the approximate solution with fast convergence rate and high accuracy in the case of solitary wave solution and closed… (More)

- Magdy A. El-Tawil, Noha A. Al-Mulla
- Mathematical and Computer Modelling
- 2010

The homotopy analysis method (HAM) is used to find approximate analytical solutions of continuous population models for single and interacting species. The homotopy analysis method contains the auxiliary parameter ~, which provides us with a simple way to adjust and control the convergence region of series solution. the solutions are compared with the… (More)

- Tamer A. Abassy, Magdy A. El-Tawil, H. El-Zoheiry
- Computers & Mathematics with Applications
- 2007

In this paper, the variational iteration method (VIM) is reintroduced with Laplace transforms and the Padé technique treatment to obtain closed form solutions of nonlinear equations. Some examples, including the coupled Burger’s equation, compacton k(n, n) equation, Zakharov–Kuznetsov Zk(n, n) equation, and KdV and mKdV equations are given to show the… (More)

- Magdy A. El-Tawil
- Applied Mathematics and Computation
- 2005

- Tamer A. Abassy, Magdy A. El-Tawil, H. El-Zoheiry
- Computers & Mathematics with Applications
- 2007

The convergence of qhomotopy analysis method (q-HAM) is studied in the present paper. It is proven that under certain conditions the solution of the equation: 1 ∅ , ∅ , 0 associated with the original problem exists as a power series in .So,under a special constraint the q-homotopy analysis method does converge to the exact solution of nonlinear problems. An… (More)

- Hany N. Hassan, Magdy A. El-Tawil
- Applied Mathematics and Computation
- 2012

- Magdy A. El-Tawil, Mohammed A. Sohaly
- 2011

Randomness may exist in the initial value or in the differential operator or both. In [1,2], the authors discussed the general order conditions and a global convergence proof is given for stochastic Runge-Kutta methods applied to stochastic ordinary differential equations (SODEs) of Stratonovich type. In [3,4], the authors discussed the random Euler method… (More)