Article Traveling Wave Solutions of Seventh-order Generalized KdV Equations Using He's Polynomials was published on February 1, 2009 in the journal International Journal Nonlinear Sciences and Numerical Simulation (volume 10, issue 2).

We apply the homotopy perturbation method for solving fourth-order boundary value problems. The analytical results of problems have been obtained in terms convergent series with easily computable components. Several examples are given to illustrate efficiency and implementation method. Comparisons made confirm reliability Homotopy can be considered an alternative Adomian decomposition its variant forms.

This paper outlines a detailed study of some relatively new techniques which are originated by He for solving diversified nonlinear problems physical nature. In particular, we will focus on the variational iteration method (VIM) and its modifications, homotopy perturbation (HPM), parameter expansion method, exp‐function method. These but very reliable proved useful wide class capable to cope with versatility problems. Several examples given reconfirm efficiency these algorithms. Some open...

Article Variational Iteration Method for Solving Higher-order Nonlinear Boundary Value Problems Using He's Polynomials was published on June 1, 2008 in the journal International Journal of Sciences and Numerical Simulation (volume 9, issue 2).

Abstract We apply a relatively new technique which is called the homotopy perturbation method (HPM) for solving linear and nonlinear partial differential equations. The suggested algorithm quite efficient practically well suited use in these problems. proposed iterative scheme finds solution without any discretization, linearization or restrictive assumptions. Several examples are given to verify reliability efficiency of method. fact that HPM solves problems using Adomian’s polynomials can...

In this article, a novel (G'/G)-expansion method is proposed to search for the traveling wave solutions of nonlinear evolution equations. We construct abundant involving parameters Boussinesq equation by means suggested method. The performance reliable and useful, gives more general exact than existing methods. new provides not only forms but also cuspon, peakon, soliton, periodic waves.

We have computed new exact traveling wave solutions, including complex solutions of fractional order Boussinesq-Like equations, occurring in physical sciences and engineering, by applying Exp-function method. The method is blended with transformation modified Riemann-Liouville operator. Our obtained are verified substituting back into their corresponding equations. To the best our knowledge, no other technique has been reported to cope said nonlinear problems combined variety solutions....

Abstract The investigation of thermal performance in the nanofluids for unsteady boundary layer flow by considering impacts suction/injection is a significant research area field fluid dynamics. This situation broadly used aerodynamics and space sciences as well. model formulated ND-H 2 O Ag-H then tackled numerically captured dynamics under multiple parameters. From results, it investigated that both have high characteristics. However, higher heat transfer observed Ag based nanofluid....

This article is dedicated to analyzing the heat transfer in flow of water-based nanofluids a channel with non-parallel stretchable walls. The magnetohydrodynamic (MHD) nature considered. Equations governing are transformed into system nonlinear ordinary differential equations. said solved by employing two different techniques, variational iteration method (VIM) and Runge-Kutta-Fehlberg (RKF). influence emerging parameters on velocity temperature profiles highlighted help graphs coupled...

We have investigated a two-dimensional radiative flow of boundary layer nature. The fluid under consideration is carbon nanotube (CNT)-based nanofluid and it flows over curved surface. heat transfer through the analyzed influence internal generation. Water (base fluid) along with single or multi-walled nanotubes taken to compose nanofluid. After introducing suitable similarity variables, consequent equations are reduced system nonlinear ordinary differential equations. solution computed by...

In this work, we have implemented a direct method, known as Khater method to establish exact solutions of nonlinear partial differential equations fractional order. Number provided by is greater than other traditional methods. Exact order Sharma Tasso-Olever (STO) equation are expressed in terms kink, travelling wave, periodic and solitary wave solutions. Modified Riemann-Liouville derivative Fractional complex transform been used for compatibility with sense. Solutions graphically simulated...

An innovative concept of water-based Cu–Al2O3 hybrid nanofluid has been employed to investigate the behavior flow and heat transfer inside a rectangular channel whose permeable walls experiences dilation or contraction in height. The transformed set ordinary differential equations is then solved by well-known Runge–Kutta–Fehlberg algorithm. analysis also includes three different shapes copper nanocomposites, namely, platelet, cylinder brick- shaped. impact various embedded parameters on...

Squeezing flow of nanofluids has been taken into account under the effects viscous dissipation and velocity slip. Two types base fluids are used to study behavior Copper nanoparticles between parallel plates. Nonlinear ordinary differential equations governing obtained by imposing similarity transformations on conservation laws. Resulting solved using an efficient analytical technique variation parameters method (VPM). Influences nanoparticle concentration different emerging profiles...