In this paper, the piecewise homotopy perturbation method (PHPM) is employed to solve the Hamilton– Jacobi–Bellman (HJB) equation arising in the optimal control problems. The method is a simple modification of the standard homotopy perturbation method (HPM), in which it is treated as an algorithm in a sequence of small intervals (i.e. time step) for finding accurate approximate solutions to the...

Mathematical models are presented in this paper to describe human maneuvers for aircraft flight simulation. Input parameters for the human pilot model (HPM), such as the course deviation indicator (CDI) and the heading change, are defined for the model, and are related mathematically to those in the proportional-integral-derivative (PID) controller for automatic control. Similarities are discus...

Two series of banana-shaped liquid crystalline (LC) H-bonded complexes HPm/CBn (i.e., bent-core H-bonded sidechain homopolymer HP mixed with bent-core covalent-bonded small molecule CB) and CPm/HBn (i.e., bent-core covalent-bonded side-chain homopolymer CP mixed with bent-core H-bonded small molecular complex HB) with various m/n molar ratios were developed. The bent-core covalentand H-bonded s...

This paper presents a study of transport parameters (diffusion, dynamic permeability, thermal permeability, trapping constant) of porous media by combining the homogenization of periodic media (HPM) and the self-consistent scheme (SCM) based on a bicomposite spherical pattern. The link between the HPM and SCM approaches is first established by using a systematic argument independent of the prob...

"Compulsory Education Mathematics Curriculum Standards (2022 Edition)" clearly states that attention should be paid to mathematics culture, but at present, textbooks and classrooms still do not attach importance culture is really integrated into classroom teaching. For further exploring how integrate mathematical teaching, the traditional teaching design of Letters Represent Numbers transformed...

The Hierarchical Predictive Model (HPM) is a semiparametric mixed model where the fixed effects are fit with a user-specified non-parametric component. This approach extends current spline-based semiparametric mixed model formulations, allowing for more flexible nonparametric estimation. Greater adaptability simplifies model specification making it easier to analyze data sets with large numbers...

In this paper, the homotopy analysis method (HAM) proposed by Liao in 1992 and the homotopy perturbation method (HPM) proposed by He in 1998 are compared through an evolution equation used as the second example in a recent paper by Ganji et al (2007). It is found that the HPM is a special case of the HAM when ~ = −1. However, the HPM solution is divergent for all x and t except t = 0. It is als...

In this paper, the homotopy perturbation method (HPM) is considered for finding approximate solutions of two-dimensional viscous flow. This technique provides a sequence of functions which converges to the exact solution of the problem. The HPM does not need a small parameters in the equations, but; the perturbation method depends on small parameter assumption and the obtained results. In most ...

Abstract: This study focus on the solution of the generalized Korteweg and de Vries (KdV) by using homotopy perturbation method (HPM). The HPM has the capabilities to bereave the complicated differential equation models to number of simple iterative models once the effective initial guess satisfying the boundary conditions is made and leads to generic solutions in addition to their rapid conver...

Generalized approximation technique for a solution of one-dimensional steady state heat transfer problem in a slab made of a material with temperature dependent thermal conductivity, is developed. The results obtained by the generalized approximation method (GAM) are compared with those studied via homotopy perturbation method (HPM). For this problem, the results obtained by the GAM are more ac...