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Article
Publication date: 20 February 2020

Ji-Huan He and Habibolla Latifizadeh

The purpose of this paper is to suggest a general numerical algorithm for nonlinear problems by the variational iteration method (VIM).

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Abstract

Purpose

The purpose of this paper is to suggest a general numerical algorithm for nonlinear problems by the variational iteration method (VIM).

Design/methodology/approach

Firstly, the Laplace transform technique is used to reconstruct the variational iteration algorithm-II. Secondly, its convergence is strictly proved. Thirdly, the numerical steps for the algorithm is given. Finally, some examples are given to show the solution process and the effectiveness of the method.

Findings

No variational theory is needed to construct the numerical algorithm, and the incorporation of the Laplace method into the VIM makes the solution process much simpler.

Originality/value

A universal iteration formulation is suggested for nonlinear problems. The VIM cleans up the numerical road to differential equations.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 11
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 1 January 2014

Yasir Khan and Habibolla Latifizadeh

The purpose of this paper is to introduce a new modified version of the homotopy perturbation method (NMHPM) and Adomian decomposition method (ADM) for solving the nonlinear…

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Abstract

Purpose

The purpose of this paper is to introduce a new modified version of the homotopy perturbation method (NMHPM) and Adomian decomposition method (ADM) for solving the nonlinear ordinary differential equation arising in MHD non-Newtonian fluid flow over a linear stretching sheet.

Design/methodology/approach

The governing equation is solved analytically by applying a newly developed optimal homotopy perturbation approach and ADM. This optimal approach contains convergence-control parameter and is computationally rather efficient. The results of numerical example are presented and only a few terms are required to obtain accurate solutions.

Findings

A new modified optimal and ADM methods accelerate the rapid convergence of the series solution. These methods dramatically reduce the size of work. The obtained series solution is combined with the diagonal Padé approximants to handle the boundary condition at infinity. Results derived from these methods are shown graphically and in tabulated forms to study the efficiency and accuracy.

Practical implications

Non-Newtonian flow processes play a key role in many types of polymer engineering operations. The formulation of mathematical model for these processes can be based on the equations of non-Newtonian fluid mechanics. The flow of an electrically conducting fluid in the presence of a magnetic field is of importance in various areas of technology and engineering such as MHD power generation, MHD flow meters, MHD pumps, etc. It is generally admitted that a number of astronomical bodies (e.g. the sun, Earth, Jupiter, Magnetic stars, Pulsars) posses fluid interiors and (or least surface) magnetic fields.

Originality/value

The present results are original and new for the MHD non-Newtonian fluid flow over a linear stretching sheet. The results attained in this paper confirm the idea that NMHPM and ADM are powerful mathematical tools and that can be applied to a large class of linear and nonlinear problems arising in different fields of science and engineering.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 24 no. 1
Type: Research Article
ISSN: 0961-5539

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