Sefa Anıl Sezer

Effects of partial slip on the peristaltic flow of a MHD Newtonian fluid in an asymmetric channel

In this study, the effects of partial slip on the peristaltic flow of a MHD Newtonian fluid in an asymmetric channel are studied analytically and numerically. The governing equations of motion and energy are simplified using a long wavelength approximation. A closed form solution of the momentum equation is obtained by the homotopy perturbation method (HPM) and an exact solution of the energy equation is presented in the presence of the viscous dissipation term. The expression for pressure rise is calculated using numerical integration. Also, we discussed the trapping phenomena. The graphical results are presented to interpret various physical parameter of interest.

Numerical soliton solutions of improved Boussinesq equation

Purpose – The purpose of this paper is to use the homotopy perturbation method (HPM) to obtain numerical soliton solution of the improved Boussinesq equation (IBE). The solutions are calculated in the form of a convergent power series with easily computable components.Design/methodology/approach – The HPM is used to obtain numerical soliton solution of the IBE. The solutions are calculated in the form of a convergent power series with easily computable components.Findings – The errors are obtained by using the approximate solution given by using only two iterations of the HPM. It is evident that the efficiency of this approach can be dramatically enhanced by computing further terms of approximate solution.Originality/value – The numerical results presented in the paper show that only a few terms are sufficient to obtain accurate solutions.

HE'S HOMOTOPY PERTURBATION METHOD FOR SOLVING THE FRACTIONAL KDV-BURGERS-KURAMOTO EQUATION

Purpose – 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.Design/methodology/approach – The authors used Maple Package to calculate the functions obtained from the HPM.Findings – The fractional derivatives are described in the Caputo sense. HPM performs extremely well in terms of accuracy, efficiently, simplicity, stability and reliability.Originality/value – The paper describes how the HPM has been successfully applied to find the solution of fractional KdV‐Burgers‐Kuramoto equation.

Modified Variational Iteration Method for Free-Convective Boundary-Layer Equation Using Padé Approximation

This paper is devoted to the study of a free-convective boundary-layer flow modeled by a system of nonlinear ordinary differential equations. We apply a modified variational iteration method (MVIM) coupled with Hes polynomials and Pade approximation to solve free-convective boundary-layer equation. It is observed that the combination of MVIM and the Pade approximation improves the accuracy and enlarges the convergence domain.

Non-Perturbative Solution of the Magnetohydrodynamic Flow over a Nonlinear Stretching Sheet by Homotopy Perturbation Method-Padé Technique

In this study, we investigate the magnetohydrodynamic (MHD) boundary layer flow by employing the homotopy perturbation method (HPM) and Pad´e approximation. The series solution of the governing nonlinear problem is developed. Generally, the truncated series solution is adequate only in a small region when the exact solution is not reached. We overcame this limitation by using the Pad´e techniques, which have the advantage in turning the polynomials approximation into a rational function, and applied it to the series solution to improve the accuracy and enlarge the convergence domain. A comparison of the present solution with the existing solution is made and excellent agreement is noted.

Analytical Approach to a Slowly Deforming Channel Flow with Weak Permeability

In this paper, we develop the analytical solution of the Navier-Stokes equations for a semi-infinite rectangular channel with porous and uniformly expanding or contracting walls by employing the homotopy perturbation method (HPM). The series solution of the governing problem is obtained. Some examples have been included. The results so obtained are compared with the existing literature and a remarkable improvement leads to an excellent agreement with the numerical results.

Numerical Solutions of Fourth-Order Fractional Integro-Differential Equations

In this paper, the homotopy perturbation method (HPM) is developed to obtain numerical solutions of linear and nonlinear boundary value problems for fourth-order fractional integro-differential equations. The fractional derivatives are described in the Caputo sense. Some examples are given and comparisons are made; the comparisons show that the homotopy perturbation method is very effective and convenient and overcome the difficulty of traditional methods. Numerical examples are presented to illustrate the efficiency, simplicity, and reliability of the method.