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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)

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)

In this paper, a more general method of homotopy analysis method (HAM) is introduced to solve non-linear differential equations, it is called (q-HAM). The interval of convergence of HAM, if exists, is increased when using q-HAM. The analysis shows that the series solution in the case of q-HAM is more likely to converge than that on HAM. The new method is… (More)

The convergence of q-homotopy analysis method (q-HAM) is studied in the present paper. It is proven that under certain conditions the solution of the equation: ሺ1 െ ݊ݍሻሾܮሺ∅ሺ,ݐ ݍሻሻ െ ܮሺݑ ሻሿ െ ݄ܰݍሾ∅ሺ,ݐ ݍሻሿ ൌ 0 associated with the original problem exists as a power series in .ݍSo,under a special constraint the q-homotopy analysis method… (More)

under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract The homotopy analysis method (HAM) is used to find approximate analytical solutions of continuous population models for single and interacting species. The homotopy analysis… (More)