Daftardar-Jafari Method Research Articles

Daftardar-Jafari method for solving nonlinear thin film flow problem

The aim of this paper is to develop the Daftardar-Jafari iterative method (DJM) for a mathematical model that represents the nonlinear thin film flow of a non-Newtonian third-grade fluid on a moving belt with the aim to obtain an approximate solution of high accuracy. When applying the DJM there is no need to resort to any additional techniques such as evaluating Adomian’s polynomials as in the Adomian decomposition method (ADM) or such as using Lagrange multipliers in the variational iteration method (VIM). The accuracy of our results is numerically verified by evaluating the functions of the error remainder and the maximal error remainders. In addition, these results are analyzed by comparing the accuracy of the DJM solutions with those of the fourth order Runge-Kutta method (RKM), ADM and VIM at the same parameter values. All the evaluations have been successfully performed in an iterative way by using the symbolic manipulator Mathematica®.

Analytic and numerical solution for duffing equations

Daftardar Gejji and Hossein Jafari have proposed a new iterative method for solving many of the linear and nonlinear equations namely (DJM). This method proved already the effectiveness in solved many of the ordinary differential equations, partial differential equations and integral equations. The main aim from this paper is to propose the Daftardar-Jafari method (DJM) to solve the Duffing equations and to find the exact solution and numerical solutions. The proposed (DJM) is very effective and reliable, and the solution is obtained in the series form with easily computed components. The software used for the calculations in this study was MATHEMATICA® 9.0.

Analytic Comparison of MHD Squeezing Flow in Porous Medium with Slip Condition

The aim of this paper is to compare the efficiency of various techniques for squeezing flow of an incompressible viscous fluid in a porous medium under the influence of a uniform magnetic field squeezed between two large parallel plates having slip boundary. Fourth-order nonlinear ordinary differential equation is obtained by transforming the Navier-Stokes equations. Resulting boundary value problem is solved using Differential Transform Method (DTM), Daftardar Jafari Method (DJM), Adomian Decomposition Method (ADM), Homotopy Perturbation Method (HPM), and Optimal Homotopy Asymptotic Method (OHAM). The problem is also solved numerically using Mathematica solver NDSolve. The residuals of the problem are used to compare and analyze the efficiency and consistency of the abovementioned schemes.

A decomposition method for solving diffusion equations via local fractional time derivative

In this paper a decomposition method based on Daftardar-Jafari method is applied for solving diffusion equations involving local fractional time derivatives. The convergence of this method for solving these type of equations is proved.

Numerical Solutions of Fifth and Sixth Order Nonlinear Boundary Value Problems by Daftardar Jafari Method

Fifth and sixth order boundary value problems are solved using Daftardar Jafari method (DJM). DJM is introduced by Daftardar-Gejji and Jafari (2006). The approach provides the solution in the form of a rapidly convergent series. The comparison among Daftardar Jafari method (DJM), Adomian decomposition method (ADM), homotopy perturbation method (HPM), variation iteration method (VIM), and the iterative method (ITM) are displayed in table form which shows the efficiency of DJM for the solution of fifth and sixth order BVPs.

Application of Daftardar Jafari Method to First Grade MHD Squeezing Fluid Flow in a Porous Medium with Slip Boundary Condition

In the present work, in the presence of magnetic field and with slip boundary condition, squeezing flow of a Newtonian fluid in a porous medium between two large parallel plates is investigated. The governing equations are transformed to a single nonlinear boundary value problem. Daftardar Jafari Method (DJM) is used to solve the problem in order to obtain the velocity profile of the fluid. By using residual of the problem, the validity of solution is established. The velocity profile is argued through graphs for various values of parameters.