A key aspect of the recently proposed Hamiltonian Particle-Mesh (HPM) method is its time-staggered discretization combined with a regularization of the continuous governing equations. In this paper, the time discretization aspect of the HPM method is analysed for the linearized, rotating, shallow-water equations with orography and the combined effect of time-staggering and regularization is com...

To obtain approximate-exact solutions to nonlocal initial-boundary value problems (IBVPs) of linear and nonlinear parabolic hyperbolic partial differential equations (PDEs) subject initial boundary conditions integral type, the homotopy perturbation method (HPM) is utilized in this study. The HPM used solve specified IBVPs, which are then transformed into local Dirichlet IBVPs. Some examples de...

In this paper, an analytical approximation to the solution of higher order Korteweg-de Vries (KdV) equations has been studied. The Homotopy Perturbation Method (HPM) introduced by He is employed to drive this analytical solution and the results will be compared with those of the Adomian decomposition method. Numerical results reveal that the HPM provides highly accurate numerical solutions for ...

We comment on the new trend in mathematical physics that consists of obtaining Taylor series for fabricated linear and nonlinear unphysical models by means of homotopy perturbation method (HPM), homotopy analysis method (HAM) and Adomian decomposition method (ADM). As an illustrative example we choose a recent application of the HPM to a dynamic system of anisotropic elasticity.

In this paper, He’s homotopy perturbation method (HPM) is applied for solving linear programming (LP) problems. This paper shows that some recent findings about this topic cannot be applied for all cases. Furthermore, we provide the correct application of HPM for LP problems. The proposed method has a simple and graceful structure. Finally, a numerical example is displayed to illustrate the pro...

Practical machine translation must be considered from a heuristic point of view rather than from a purely rigid analytical l inguistic method. An English-into-Japanese translation system named ATHENE based on a Heuristic Parsing Model (HPM) has been developed. The experiment shows some advantageous points such as simplification of transforming and generating phase, semilocalization of multiple ...

In this work, the Blasius equation is studied. Homotopy perturbation method (HPM) and homotopy analysis method (HAM) are applied to obtain its solution. Comparison with variational iteration method (VIM) is made to highlight the significant features of employed methods and their capability of handling nonlinear problems. The outcome shows the success of (HPM) and (HAM) for solving nonlinear pro...

We propose a simple heuristic partition method (HPM) of classification tree to improve efficiency in the search for splitting points of numerical attributes. The proposal is motivated by the idea that the selection process of candidates in the splitting point selection can be made more flexible as to achieve a faster computation while retaining classification accuracy. We compare the performanc...

In this paper, we conduct a comparative study between the homotopy perturbation method (HPM) and Adomian’s decomposition method (ADM) for analytic treatment of nonlinear Volterra integral equations, and we show that the HPM with a specific convex homotopy is equivalent to the ADM for these type of equations.

In this paper , we have presented Homotopy Perturbation Method (HPM) to solve nonlinear parabolic equation with nonlocal boundary conditions. This method provides an analytical solution by utilizing only the initial condition. The HPM allows for the solution of the nonlinear parabolic equations to be calculated in the form of a series with easily computable components. The obtained results are ...