Search results

The main purpose of this paper is to find convenient methods to solve the differential‐algebraic equations which have great importance in various fields of science and engineering.

The paper applies a semi‐analytical approach, using both the homotopy analysis method (HAM) and the modified homotopy analysis method (MHAM) for finding the solution of linear and nonlinear DAEs.

The results show that the new modification can effectively reduce computational costs and accelerates the rapid convergence of the series solution.

Some high index DAEs are investigated to present a comparative study between the HAM and the MHAM.

The purpose of this paper is to report the effect of radiation on flow of a magneto‐micropolar fluid past a continuously moving plate with suction and blowing.

The governing equations are transformed into dimensionless nonlinear ordinary differential equations by similarity transformation. Analytical technique, namely the homotopy perturbation method (HPM) combining with Padé approximants and finite difference method, are used to solve dimensionless non‐linear ordinary differential equations. The skin friction coefficient and local Nusselt numbers are also calculated. Beside this, the comparison of the analytical solution with numerical solution is illustrated by the graphs for different values of dimensionless pertinent parameters.

The authors have studied laminar magneto‐micropolar flow in the presence of radiation by using HPM‐Padé and finite difference methods. Results obtained by HPM‐Padé are in excellent agreement with the results of numerical solution.

The HPM‐Padé is used in a direct way without using linearization, discritization or restrictive assumption. The authors have attempted to show the capabilities and wide‐range applications of the HPM‐Padé in comparison with the finite difference solution of magneto‐micropolar flow in the presence of radiation problem.

The purpose of this paper is to apply He's variational iteration method (VIM) coupled with an auxiliary parameter, which proves very effective to control the convergence region of approximate solution.

The proposed algorithm is tested on generalized Hirota‐Satsuma coupled KdV equation.

Numerical results explicitly reveal the complete reliability, efficiency and accuracy of the suggested technique.

It is observed that the approach may be implemented on other nonlinear models of physical nature.

This paper aims to directly extend the homotopy perturbation method to study the coupled Burgers equations with time‐ and space‐fractional derivatives.

The realistic numerical solutions were obtained in a form of rapidly convergent series with easily computable components.

The figures show the effectiveness and good accuracy of the proposed method.

The paper obtains realistic numerical solutions in a form of rapidly convergent series with easily computable components. It shows the effectiveness and good accuracy of the proposed method.

The purpose of this paper is to directly extend the homotopy perturbation method (HPM) that was developed for integer‐order differential equation, to derive explicit and numerical solutions of the fractional KdV‐Burgers‐Kuramoto equation.

The authors used Maple Package to calculate the functions obtained from the HPM.

The fractional derivatives are described in the Caputo sense. HPM performs extremely well in terms of accuracy, efficiently, simplicity, stability and reliability.

The paper describes how the HPM has been successfully applied to find the solution of fractional KdV‐Burgers‐Kuramoto equation.

The purpose of this paper is to obtain soliton solution of the Kaup‐Kupershmidt (KK) equation with initial condition. The most important feature of this method is to obtain the solution without direct transformation.

In this paper, the homotopy perturbation method (HPM) is used for obtaining soliton solution of the KK equation. The numerical solutions are compared with the known analytical solutions. The results of numerical examples are presented and only a few terms are required to obtain accurate solutions. Results derived from this method are shown graphically.

The authors obtained the one soliton solution for the KK equation by HPM. The numerical results showed that this method is very accurate. The HPM provides a reliable technique that requires less work if compared with the traditional techniques and the method does not also require unjustified assumptions, linearization, discretization or perturbation. The HPM is very easily applied to both differential equations and linear or nonlinear differential systems.

The paper describes how the authors obtained one soliton solution for the KK equation by HPM. The numerical results presented show that this method is very accurate.

The purpose of this paper is to consider analytical solution of wave system in Rⁿ with coupling controllers by using the homotopy perturbation method (HPM).

HPM is applied to the system of linear partial differential equations, i.e. the system of waves in the two‐dimensional version of system equations (1) and (2). This problem is motivated by an analogous problem in ordinary differential equations for coupled oscillators and has potential application in isolating a vibrating object from the outside disturbances. For example, rubber or rubber‐like materials can be used to either absorb or shield a structure from vibration. As an approximation, these materials can be modeled as distributed springs.

In this paper, HPM was used to obtain analytical solution of wave system in with coupling controllers. The method provides the solutions in the form of a series with easily computable terms. Unlike other common methods for solving any physical problem, linear or nonlinear, that requires linearization, discretization, perturbation, or unjustified assumptions that may slightly change the physics of the problem, the HPM finds approximate analytical solutions by using the initial conditions only.

The method proposed in this paper is very reliable and efficient and is being used quite extensively for diversified nonlinear problems of a physical nature. The algorithm is being used for the first time on such problems.

This paper aims to discuss the approximate solution of the nonlinear thin film flow problems. A new analytic approximate technique for addressing nonlinear problems, namely, the optimal homotopy asymptotic method (OHAM), is proposed and used in an application to the nonlinear thin film flow problems.

This approach does not depend upon any small/large parameters. This method provides a convenient way to control the convergence of approximation series and to adjust convergence regions when necessary.

The obtained solutions show that the OHAM is more effective, simpler and easier than other methods. The results reveal that the method is explicit. By applying the method to nonlinear thin film flow problems, it was found to be simpler in applicability, and more convenient to control convergence. Therefore, the method shows its validity and great potential for the solution of nonlinear problems in science and engineering.

The proposed method is tested upon nonlinear thin film flow equation from the literature and the results are compared with the available approximate solutions including Adomian decomposition method (ADM), homotopy perturbation method, modified homotopy perturbation method and HAM. Moreover, the exact solution is compared with the available numerical solutions. The graphical representation of the solution is given by Maple and is physically interpreted.

The purpose of this paper is to develop an efficient method for solving the magneto-hydrodynamic (MHD) boundary layer flow of an upper-convected Maxwell (UCM) fluid over a porous isothermal stretching sheet.

The paper applied a collocation approach based on rational Legendre functions for solving the third-order non-linear boundary value problem, describing the MHD boundary layer flow of an UCM fluid over a porous isothermal stretching sheet. This method solves the problem on the semi-infinite domain without transforming domain of the problem to a finite domain.

This approach reduces the solution of a problem to the solution of a system of algebraic equations. The numerical values of the skin friction coefficient are presented and analyzed for various parameters of interest in the problem. The authors also compare the results of this work with some recent results and show that the new method is efficient and applicable.

The method solves this problem without use of discrete variables and linearization or small perturbation. Also it was confirmed by the theorem and figure of absolute coefficients that this approach has exponentially convergence rate.

This study aims to assess the impact of adopting selected green construction site practices on the health and safety performance of the construction projects. The impact of storm-water management, energy management and construction waste management on projects health and safety performance was also examined.

A survey was conducted to collect information from Class A contractors in Nigeria, and 168 usable responses were received. The data were analysed using the partial least squares (PLSs) structural equation modelling technique.

The findings indicate that energy management and waste management practices have significant effects on the health and safety performance of the construction projects, while storm-water management has no effect.

Project and site managers need to take into consideration the skill set of their workforce when attempting to adopt new innovative construction strategies the workers are unfamiliar with in a changing construction environment. There is also a need for more training of workers on generic and specific green skills to avoid health and safety challenges on site.

The findings of this study make significant contribution to the debate on the health and safety performance of green projects, as only a few studies have been conducted on this topic. The empirical relationships between the constructs of energy management, waste management, storm-water management and health and safety performance are unique in the context of other related studies and have advanced the body of existing knowledge.