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1 – 10 of 108Abbas Saadatmandi and Zeinab Sanatkar
The purpose of this paper is to develop an efficient method for solving the magneto-hydrodynamic (MHD) boundary layer flow of an upper-convected Maxwell (UCM) fluid over a porous…
Abstract
Purpose
The purpose of this paper is to develop an efficient method for solving the magneto-hydrodynamic (MHD) boundary layer flow of an upper-convected Maxwell (UCM) fluid over a porous isothermal stretching sheet.
Design/methodology/approach
The paper applied a collocation approach based on rational Legendre functions for solving the third-order non-linear boundary value problem, describing the MHD boundary layer flow of an UCM fluid over a porous isothermal stretching sheet. This method solves the problem on the semi-infinite domain without transforming domain of the problem to a finite domain.
Findings
This approach reduces the solution of a problem to the solution of a system of algebraic equations. The numerical values of the skin friction coefficient are presented and analyzed for various parameters of interest in the problem. The authors also compare the results of this work with some recent results and show that the new method is efficient and applicable.
Originality/value
The method solves this problem without use of discrete variables and linearization or small perturbation. Also it was confirmed by the theorem and figure of absolute coefficients that this approach has exponentially convergence rate.
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K. Parand and L. Hosseini
The aim is to present in this paper an effective strategy in dealing with a semi‐infinite interval by using a suitable mapping that transforms a semi‐infinite interval to a finite…
Abstract
Purpose
The aim is to present in this paper an effective strategy in dealing with a semi‐infinite interval by using a suitable mapping that transforms a semi‐infinite interval to a finite interval.
Design/methodology/approach
The authors introduce a new orthogonal system of rational functions induced by general Jacobi polynomials with the parameters alpha and beta. It is more flexible in applications. In particular, alpha and beta could be regulated, so that the systems are mutually orthogonal in certain weighted Hilbert spaces.
Findings
This approach is applied for solving a non‐linear system two‐point boundary value problem (BVP) on semi‐infinite interval, describing the flow and diffusion of chemically reactive species over a nonlinearly stretching sheet immersed in a porous medium. The new approach reduces the solution of a problem to the solution of a system of algebraic equations.
Originality/value
The paper presents an effective strategy in dealing with a semi‐infinite interval by using a suitable mapping that transforms a semi‐infinite interval to a finite interval.
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Velinda Calvert and Mohsen Razzaghi
This paper aims to propose a new numerical method for the solution of the Blasius and magnetohydrodynamic (MHD) Falkner-Skan boundary-layer equations. The Blasius and MHD…
Abstract
Purpose
This paper aims to propose a new numerical method for the solution of the Blasius and magnetohydrodynamic (MHD) Falkner-Skan boundary-layer equations. The Blasius and MHD Falkner-Skan equations are third-order nonlinear boundary value problems on the semi-infinite domain.
Design/methodology/approach
The approach is based upon modified rational Bernoulli functions. The operational matrices of derivative and product of modified rational Bernoulli functions are presented. These matrices together with the collocation method are then utilized to reduce the solution of the Blasius and MHD Falkner-Skan boundary-layer equations to the solution of a system of algebraic equations.
Findings
The method is computationally very attractive and gives very accurate results.
Originality/value
Many problems in science and engineering are set in unbounded domains. One approach to solve these problems is based on rational functions. In this work, a new rational function is used to find solutions of the Blasius and MHD Falkner-Skan boundary-layer equations.
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K. Parand, Mehdi Dehghan and A. Taghavi
The purpose of this paper is to propose a Tau method for solving nonlinear Blasius equation which is a partial differential equation on a flat plate.
Abstract
Purpose
The purpose of this paper is to propose a Tau method for solving nonlinear Blasius equation which is a partial differential equation on a flat plate.
Design/methodology/approach
The operational matrices of derivative and product of modified generalized Laguerre functions are presented. These matrices together with the Tau method are then utilized to reduce the solution of the Blasius equation to the solution of a system of nonlinear equations.
Findings
The paper presents the comparison of this work with some well‐known results and shows that the present solution is highly accurate.
Originality/value
This paper demonstrates solving of the nonlinear Blasius equation with an efficient method.
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Mohammad Heydari, Ghasem Barid Loghmani and Abdul-Majid Wazwaz
The main purpose of this paper is to implement the piecewise spectral-variational iteration method (PSVIM) to solve the nonlinear Lane-Emden equations arising in mathematical…
Abstract
Purpose
The main purpose of this paper is to implement the piecewise spectral-variational iteration method (PSVIM) to solve the nonlinear Lane-Emden equations arising in mathematical physics and astrophysics.
Design/methodology/approach
This method is based on a combination of Chebyshev interpolation and standard variational iteration method (VIM) and matching it to a sequence of subintervals. Unlike the spectral method and the VIM, the proposed PSVIM does not require the solution of any linear or nonlinear system of equations and analytical integration.
Findings
Some well-known classes of Lane-Emden type equations are solved as examples to demonstrate the accuracy and easy implementation of this technique.
Originality/value
In this paper, a new and efficient technique is proposed to solve the nonlinear Lane-Emden equations. The proposed method overcomes the difficulties arising in calculating complicated and time-consuming integrals and terms that are not needed in the standard VIM.
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Umesh and Manoj Kumar
The purpose of this paper is to obtain the highly accurate numerical solution of Lane–Emden-type equations using modified Adomian decomposition method (MADM) for unequal step-size…
Abstract
Purpose
The purpose of this paper is to obtain the highly accurate numerical solution of Lane–Emden-type equations using modified Adomian decomposition method (MADM) for unequal step-size partitions.
Design/methodology/approach
First, the authors describe the standard Adomian decomposition scheme and the Adomian polynomials for solving nonlinear differential equations. After that, for the fast calculation of the Adomian polynomials, an algorithm is presented based on Duan’s corollary and Rach’s rule. Then, MADM is discussed for the unequal step-size partitions of the domain, to obtain the numerical solution of Lane–Emden-type equations. Moreover, convergence analysis and an error bound for the approximate solution are discussed.
Findings
The proposed method removes the singular behaviour of the problems and provides the high precision numerical solution in the large effective region of convergence in comparison to the other existing methods, as shown in the tested examples.
Originality/value
Unlike the other methods, the proposed method does not require linearization or perturbation to obtain an analytical and numerical solution of singular differential equations, and the obtained results are more physically realistic.
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Michael Chapwanya, Robert Dozva and Gift Muchatibaya
This paper aims to design new finite difference schemes for the Lane–Emden type equations. In particular, the authors show that the schemes are stable with respect to the…
Abstract
Purpose
This paper aims to design new finite difference schemes for the Lane–Emden type equations. In particular, the authors show that the schemes are stable with respect to the properties of the equation. The authors prove the uniqueness of the schemes and provide numerical simulations to support the findings.
Design/methodology/approach
The Lane–Emden equation is a well-known highly nonlinear ordinary differential equation in mathematical physics. Exact solutions are known for a few parameter ranges and it is important that any approximation captures the properties of the equation it represent. For this reason, designing schemes requires a careful consideration of these properties. The authors apply the well-known nonstandard finite difference methods.
Findings
Several interesting results are provided in this work. The authors list these as follows. Two new schemes are designed. Mathematical proofs are provided to show the existence and uniqueness of the solution of the discrete schemes. The authors show that the proposed method can be extended to singularly perturbed equations.
Originality/value
The value of this work can be measured as follows. It is the first time such schemes have been designed for the kind of equations.
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Oscar A.G. de Suarez, Rodrigo Rossi and Cláudio R.A. da Silva
The purpose of this paper is to investigate the approximation performance of a family of piecewise rational polynomial shape functions, which are enriched by a set of monomials of…
Abstract
Purpose
The purpose of this paper is to investigate the approximation performance of a family of piecewise rational polynomial shape functions, which are enriched by a set of monomials of order p to obtain high order approximations. To numerically demonstrate the features of the enriched approximation some examples on the mechanical elastic response and free‐vibration of axisymmetric plates and shells are carried out.
Design/methodology/approach
The global approximation is based on a particular family of weight function, which is defined on the parametric domain of the element, ξ∈[−1,1], resulting in shape functions with compact support, which have regularity C0k,k=0,2,4… in the global domain Σ. The PU shape functions are enriched by a set of monomials of order p to obtain high order approximation spaces.
Findings
Based on the numerical results of elastic axisymmetric plates and shells, it is demonstrated that the proposed methodology produces satisfactory results in terms of keeping the ill‐conditioning of the system of equations under accepted levels. Comparisons are established between linear and Hermitian shape functions showing similar results. The observed results for the free‐vibration problem of plates and shells show the potential of the proposed approximation space.
Research limitations/implications
In this paper the formulation is limited to the modeling of axisymmetric plate and shell problems. However, it can be applied to model other problems where the high regularity of the approximation is required.
Originality/value
The paper presents an alternative approach to construct partition of unity shape functions based on a particular family of weight function.
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Thibault de Swarte and Alain Amintas
The analysis of organizations has a debt vis-à-vis the sociologist Max Weber who built its theoretical foundations. The concept of limited rationality was later proposed by…
Abstract
The analysis of organizations has a debt vis-à-vis the sociologist Max Weber who built its theoretical foundations. The concept of limited rationality was later proposed by Herbert Simon and then followed by sociologists of organizations. This paper tries to go beyond that approach. It uses a psychoanalytical perspective based on Jacques Lacan's work and on the case studies of two high-tech companies. We focus on signifiers and the role of the unconscious process inside organizations. We then propose an alternative model of interpretation of organizational dynamics different from the mainstream, which is dominated by the reference to instrumental rationality.
Suvranu De and Klaus‐Jürgen Bathe
Computational efficiency and reliability are clearly the most important requirements for the success of a meshless numerical technique. While the basic ideas of meshless…
Abstract
Computational efficiency and reliability are clearly the most important requirements for the success of a meshless numerical technique. While the basic ideas of meshless techniques are simple and well understood, an effective meshless method is very difficult to develop. The efficiency depends on the proper choice of the interpolation scheme, numerical integration procedures and techniques of imposing the boundary conditions. These issues in the context of the method of finite spheres are discussed.
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