In this paper, we apply the homotopy perturbation method (HPM) for solving the Cauchy problems of the first-order partial differential equation. We obtain the exact solutions to the homogeneous or inhomogeneous linear and nonlinear equations. Numerical results are presented to confirm the efficiency of the HPM. Mathematics Subject Classification: 35K15, 35C05, 65D99, 65M99

We implement the hydro-PM (HPM) technique (Gnedin & Hui 1998) in the hydrodynamical simulation code GADGET-2 and quantify the differences between this approximate method and full hydrodynamical simulations of the Lyman-α forest in a concordance ΛCDM model. At redshifts z = 3 and z = 4, the differences between the gas and dark matter (DM) distributions, as measured by the one-point distribution ...

A novel 12-molybdophosphoric acid (HPM)-based complex (H2PI)2(H3O)[PMo12O40] [Mo2O5(H2O)2(PI)2]·11H2O (PI-HPM) was prepared by modification with picolinic acid (HPI) and characterized by the methods of Fourier transform infrared (FTIR) spectroscopy, thermogravimetry (TG), X-ray powder and single crystal diffraction. The complex retained the classical Keggin structure of bulk HPM, there were som...

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...

This paper presents an effective adaptation of an existing speaking rate-dependent hierarchical prosodic model (SRHPM) for Mandarin to construct the SR-HPM for Hakka, another Chinese dialect. Based on the cross-dialectal linguistic similarities in terms of syntactic and prosodic structures, the adaptation is formulated as a maximum a posteriori estimation (MAP) problem with the existing Mandari...

In this paper, we present homotopy perturbation method (HPM) for solving the Korteweg-de Vries (KdV) equation and convergence study of homotopy perturbation method for nonlinear partial differential equation. We compared our solution with the exact solution and homotopy analysis method (HAM). The results show that the HPM is an appropriate method for solving nonlinear equation.

Cell and animal studies have demonstrated that circadian rhythm is governed by autonomous rhythmicity of clock genes. Although disturbances in circadian rhythm have been implicated in metabolic disease development, it remains unknown whether muscle circadian rhythm is altered in human models of type 2 diabetes. Here we used human primary myotubes (HPM) to investigate if rhythmicity of clock- an...

The EEG from frontal cortex, EMG and EOG were recorded from rats exposed to only exercise (Treadmill), only stress, exercise + stress and neither (control). In comparison with the control group, the percent of Delta activity in the awake was significantly increased in the depressed group and significantly decreased in the exercised groups, while for Beta-2, the reverse occurred; Theta increased...

The HPM (Heuristic Procedure Modification) system is a model of strategy learning and optimization, implemented as a processing environment within the PRISM production system package [4]. This paper describes progress in getting HPM to emulate children's discoveries about basic addition procedures. HPM s goal-trace and production trace formalisms allow it to maintain a history of its actions wh...

The nonlinear two-dimensional forced-convection boundary-layer magneto hydrodynamic MHD incompressible flow of nanofluid over a horizontal stretching flat plate with variable magnetic field including the viscous dissipation effect is solved using the homotopy perturbation method HPM . In the present work, our results of the HPM are compared with the results of simulation using the finite differ...