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In this work, the HB method is extended to search for
similarity reduction of nonlinear partial differential equations. This method
is generalized and will apply for a (2 + 1)-dimensional higher order Broer-Kaup
System. Some new exact solutions of Broer-Kaup System are found.
In this paper, the Homotopy Analysis Method (HAM) has
been used to solve an eco-epidemic model equation. The algorithm of approximate
analytical solution is obtained. HAM contains the auxiliary parameterhwhich provides us with a convenient way
to adjust and control convergence region and rate of solution series. The
results obtained show that these algorithms are accurate and efficient for the
In this paper, we present a new method, a mixture of homotopy perturbation method and a new integral transform to solve some nonlinear partial differential equations. The proposed method introduces also He’s polynomials . The analytical results of examples are calculated in terms of convergent series with easily computed components .
In this paper, we develop a method to calculate numerical and approximate solution of some fifth-order Korteweg-de Vries equations with initial condition with the help of Laplace Decomposition Method (LDM). The technique is based on the application of Laplace transform to some fifth-order Kdv equations. The nonlinear term can easily be handled with the help of Adomian polynomials. We illustrate this technique with the help of four examples and results of the present technique have closed agreement with approximate solutions obtained with the help of (LDM).