H. Ghaneai, M.M. Hosseini and Syed Tauseef Mohyud‐Din
The purpose of this paper is to introduce an auxiliary parameter into the well‐known variational iteration algorithm which proves very effective to control the convergence region…
Abstract
Purpose
The purpose of this paper is to introduce an auxiliary parameter into the well‐known variational iteration algorithm which proves very effective to control the convergence region of approximate solution.
Design/methodology/approach
In this paper, an auxiliary parameter is introduced into the well‐known variational iteration algorithm which proves very effective to control the convergence region of approximate solution.
Findings
The present technology provides a simple way to adjust and control the convergence region of approximate solution for any values. An optimal auxiliary parameter can be obtained by the error of norm two of the residual function.
Originality/value
It is confirmed that submitted manuscript is original and is not being considered in any other journal.
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Hong-Yan Liu, Ji-Huan He and Zheng-Biao Li
Academic and industrial researches on nanoscale flows and heat transfers are an area of increasing global interest, where fascinating phenomena are always observed, e.g. admirable…
Abstract
Purpose
Academic and industrial researches on nanoscale flows and heat transfers are an area of increasing global interest, where fascinating phenomena are always observed, e.g. admirable water or air permeation and remarkable thermal conductivity. The purpose of this paper is to reveal the phenomena by the fractional calculus.
Design/methodology/approach
This paper begins with the continuum assumption in conventional theories, and then the fractional Gauss’ divergence theorems are used to derive fractional differential equations in fractal media. Fractional derivatives are introduced heuristically by the variational iteration method, and fractal derivatives are explained geometrically. Some effective analytical approaches to fractional differential equations, e.g. the variational iteration method, the homotopy perturbation method and the fractional complex transform, are outlined and the main solution processes are given.
Findings
Heat conduction in silk cocoon and ground water flow are modeled by the local fractional calculus, the solutions can explain well experimental observations.
Originality/value
Particular attention is paid throughout the paper to giving an intuitive grasp for fractional calculus. Most cited references are within last five years, catching the most frontier of the research. Some ideas on this review paper are first appeared.
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Fazhan Geng, Suping Qian and Shuai Li
– The purpose of this paper is to find an effective numerical method for solving singularly perturbed convection-diffusion problems.
Abstract
Purpose
The purpose of this paper is to find an effective numerical method for solving singularly perturbed convection-diffusion problems.
Design/methodology/approach
The present method is based on the asymptotic expansion method and the variational iteration method (VIM). First a zeroth order asymptotic expansion for the solution of the given singularly perturbed convection-diffusion problem is constructed. Then the reduced terminal value problem is solved by using the VIM.
Findings
Two numerical examples are introduced to show the validity of the present method. Obtained numerical results show that the present method can provide very accurate analytical approximate solutions not only in the boundary layer, but also away from the layer.
Originality/value
The combination of the asymptotic expansion method and the VIM is applied to singularly perturbed convection-diffusion problems.
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Mehrdad Moradnezhad and Hossein Miar Naimi
This paper aims to find a closed-form expression for the frequency and amplitude of single-ended ring oscillators when transistors experience all regions.
Abstract
Purpose
This paper aims to find a closed-form expression for the frequency and amplitude of single-ended ring oscillators when transistors experience all regions.
Design/methodology/approach
In this paper, the analytical relationships presented for ring oscillator amplitude and frequency are approximately derived due to the nonlinear nature of this oscillator, taking into account the differential equation that governs the ring oscillator and its output waveform.
Findings
In the case where the transistors experience the cut-off region, the relationships presented so far have no connection between the frequency and the dimensions of the transistor, which is not valid in practice. The relationship is presented for the frequency, including the dimensions of the transistor. Also, a simple and approximately accurate relationship for the oscillator amplitude is provided in this case.
Originality/value
The validity of these relationships has been investigated by analyzing and simulating a single-ended oscillator in 0.18 µm technology.
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– The purpose of this paper is to introduce an effective method for two-dimensional inverse heat conduction problems.
Abstract
Purpose
The purpose of this paper is to introduce an effective method for two-dimensional inverse heat conduction problems.
Design/methodology/approach
The variational iteration method (VIM) is used to solve two-dimensional inverse heat conduction problems and restore boundary conditions in heat conduction.
Findings
Numerical results compared with other methods show that the present method is remarkably effective for solving two-dimensional inverse heat conduction problems. This method is a very promoting method, which will be certainly found wide applications.
Originality/value
The VIM is applied to two-dimensional inverse heat conduction problems for the first time.
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Buhe Eerdun, Qiqige Eerdun, Bala Huhe, Chaolu Temuer and Jing-Yu Wang
The purpose of this paper is to consider a steady two-dimensional magneto-hydrodynamic (MHD) Falkner-Skan boundary layer flow of an incompressible viscous electrically fluid over…
Abstract
Purpose
The purpose of this paper is to consider a steady two-dimensional magneto-hydrodynamic (MHD) Falkner-Skan boundary layer flow of an incompressible viscous electrically fluid over a permeable wall in the presence of a magnetic field.
Design/methodology/approach
The governing equations of MHD Falkner-Skan flow are transformed into an initial values problem of an ordinary differential equation using the Lie symmetry method which are then solved by He's variational iteration method with He's polynomials.
Findings
The approximate solution is compared with the known solution using the diagonal Pad’e approximants and the geometrical behavior for the values of various parameters. The results reveal the reliability and validity of the present work, and this combinational method can be applied to other nonlinear boundary layer flow problems.
Originality/value
In this paper, an approximate analytical solution of the MHD Falkner-Skan flow problem is obtained by combining the Lie symmetry method with the variational iteration method and He's polynomials.
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Zhongfu Ren, Fanzhi Kong, Yongxiang Kang and Haiyan Kong
The purpose of this paper is to theoretically investigate the thermal and hydrodynamic performance of the flow pattern of fluid in the charged jet. The flow pattern includes…
Abstract
Purpose
The purpose of this paper is to theoretically investigate the thermal and hydrodynamic performance of the flow pattern of fluid in the charged jet. The flow pattern includes laminar flow in which all fluid layers move at different accelerated speeds, and shear forces between the fluid layers give rise to friction forces. This is a favorable condition for the parallel arrangement of the branches on polymer molecules.
Design/methodology/approach
The dynamic mechanism of the flow pattern is conducted through analyzing the forces acting on the charged jet. The differential equation obtained in the analyzing process has the solution designating the laminar flow pattern of the fluid in the charged jet.
Findings
The fluid in the charged jet flows in laminar pattern, which is favorable to the parallel arrangement of the branches on polymer molecules.
Research limitations/implications
Although the flow pattern is conveyed by means of the simple condition of uniformly accelerated motion, it has the similar effect on the arrangement of the polymer molecules in general conditions, such as non-Newtonian fluids and non-uniformly accelerated motions.
Originality/value
The laminar flow introduced by this paper to the charged jet implies anisotropic properties of the electrospun nanofibers.
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The purpose of this paper is to investigate the inverse problem of determining a time-dependent heat source in a parabolic equation with nonlocal boundary and integral…
Abstract
Purpose
The purpose of this paper is to investigate the inverse problem of determining a time-dependent heat source in a parabolic equation with nonlocal boundary and integral overdetermination conditions.
Design/methodology/approach
The variational iteration method (VIM) is employed as a numerical technique to develop numerical solution. A numerical example is presented to illustrate the advantages of the method.
Findings
Using this method, we obtain the exact solution of this problem. Whether or not there is a noisy overdetermination data, our numerical results are stable. Thus the VIM is suitable for finding the approximation solution of the problem.
Originality/value
This method is based on the use of Lagrange multipliers for the identification of optimal values of parameters in a functional and gives rapidly convergent successive approximations of the exact solution if such a solution exists.
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– The purpose of this paper is to reveal the dynamical behavior of higher dimensional nonlinear wave by searching for the multi-wave solutions to the (3+1)-D Jimbo-Miwa equation.
Abstract
Purpose
The purpose of this paper is to reveal the dynamical behavior of higher dimensional nonlinear wave by searching for the multi-wave solutions to the (3+1)-D Jimbo-Miwa equation.
Design/methodology/approach
The authors apply bilinear form and extended homoclinic test approach to the (3+1)-D Jimbo-Miwa equation.
Findings
In this paper, by using bilinear form and extended homoclinic test approach, the authors obtain new cross-kink multi-soliton solutions of the (3+1)-dimensional Jimbo-Miwa equation, including the periodic breathertype of kink three-soliton solutions, the cross-kink four-soliton solutions, the doubly periodic breather-type of soliton solutions and the doubly periodic breather-type of cross-kink two-soliton solutions. It is shown that the extended homoclinic test approach, with the help of symbolic computation, provides an effective and powerful mathematical tool for solving higher dimensional nonlinear evolution equations in mathematical physics.
Research limitations/implications
The research manifests that the structures of the solution to higher dimensional nonlinear equations are diversified and complicated.
Originality/value
The methods used in this paper can be widely applied to the research of spatial and temporal characteristics of nonlinear equations in physics and engineering technology. These methods are also conducive for people to know objective laws and grasp the essential features of the development of the world.
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Wei Chen, Hanlin Chen and Zhengde Dai
The purpose of this paper is to find solutions for the (2+1)-dimensional B-type Kadomtsev-Petviashvili equation and to research the quality of B-type Kadomtsev-Petviashvili…
Abstract
Purpose
The purpose of this paper is to find solutions for the (2+1)-dimensional B-type Kadomtsev-Petviashvili equation and to research the quality of B-type Kadomtsev-Petviashvili equation.
Design/methodology/approach
The authors apply the extended three-wave approach and the homoclinic test technique to solve the B-type Kadomtsev-Petviashvili equation.
Findings
The authors obtain breather type of cross-kink solutions, doubly breather type of kink solitary solutions and the breather type of kink wave solutions for B-type Kadomtsev-Petviashvili equation.
Research limitations/implications
As nonlinear evolution equations are characterized by rich dynamical behaviors, the authors have just found some of them and others are still to be found.
Originality/value
These results may help us to investigate the local structure and the interaction of waves in high-dimensional models.