• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1265-1277
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• 2009

In this paper, we apply a new decomposition method for solving initial and boundary value problems, which is due to Noor and Noor [18]. The analytical results are calculated in terms of convergent series with easily computable components. The diagonal Pade approximants are applied to make the work more concise and for the better understanding of the solution behavior. The proposed technique is tested on boundary layer problem; Thomas-Fermi, Blasius and sixth-order singularly perturbed Boussinesq equations. Numerical results reveal the complete reliability of the suggested scheme. This new decomposition method can be viewed as an alternative of Adomian decomposition method and homotopy perturbation methods.

• Transactions of the Korean Society of Mechanical Engineers
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• v.9 no.5
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• pp.613-620
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• 1985

An analysis on the thermal instability of horizontal Blasius flow in the form of longitudinal vortices has been carried out by introducing the 3-dimensional spatial dependence of the disturbance quantities. The stability problem has been simplified significantly by considering the limiting case of infinite Prandtl number and by skilfully replacing the boundary conditions at infinity with the interface conditions at the edge of the thermal boundary layer (or by simply confining the thermal disturbances in the thermal boundary layer). The advantage of this approach is that the critical values marking the onset of thermal instability can be readily obtained as solutions of the eigenvalues problems formulated by a 6*6(or a 5*5) determinant. Present analysis provides reasonable explanations on the existing experimental and theoretical data. Especially, the heat transfer correlation based on the present analysis agrees well with the existing experimental data.

• Communications for Statistical Applications and Methods
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• v.9 no.2
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• pp.505-514
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• 2002

Multiple correspondence analysis graphically shows the correspondent relationship among categories in multi-way contingency tables. It is well known that the proportions of the principal inertias as part of the total inertia is low in multiple correspondence analysis. Moreover, although this problem can be overcome by using the Benzecri formula, it is not enough to show clear correspondent relationship among categories (Greenacre and Blasius, 1994, Chapter 10). In addition, they show that Andrews' plot is useful in providing the correspondent relationship among categories. However, this method also does not give some concise interpretation among categories when the number of categories is large. Therefore, in this study, we will easily interpret the multiple correspondence analysis by applying the K-means clustering analysis.