• ETRI Journal
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• v.6 no.2
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• pp.18-26
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• 1984

Among the various forms of interpolating polynomial for approximation, this paper is a study about the characteristics of piecewise Lagrange interpolating polynomials. And throughout the study, an attempt is made to construct the two-dimensional ap proximating function over Rectangular Grid and Triangular Grid by using the one-dim ensional interpolating polynomials.

• Journal of the Korean Mathematical Society
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• v.43 no.2
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• pp.413-424
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• 2006

Let $\Gamma$ be a bounded rotation (BR) curve without cusps in the complex plane $\mathbb{C}$ and let G := int $\Gamma$. We prove that the rate of convergence of the interpolating polynomials based on the zeros of the Faber polynomials $F_n\;for\;\bar G$ to the function of the reflexive Smirnov-Orlicz class $E_M (G)$ is equivalent to the best approximating polynomial rate in $E_M (G)$.

• Communications of the Korean Mathematical Society
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• v.23 no.2
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• pp.295-305
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• 2008

This paper demonstrates how composite-exponential-fitting interpolation rules can be constructed to fit an oscillatory function using not only pointwise values of that function but also of that functions's derivative on a closed and bounded interval of interest. This is done in the framework of exponential-fitting techniques. These rules extend the classical composite cubic Hermite interpolating polynomials in the sense that they become the classical composite polynomials as a parameter tends to zero. Some examples are provided to compare the newly constructed rules with the classical composite cubic Hermite interpolating polynomials (or recently developed interpolation rules).

• Journal of Environmental Science International
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• v.11 no.9
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• pp.907-914
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• 2002

Various Eulerian-Lagrangian models for the one-dimensional longitudinal dispersion equation in nonuniform flow were studied comparatively. In the models studied, the transport equation was decoupled into two component parts by the operator-splitting approach; one part is governing advection and the other is governing dispersion. The advection equation has been solved by using the method of characteristics following fluid particles along the characteristic line and the results were interpolated onto an Eulerian grid on which the dispersion equation was solved by Crank-Nicholson type finite difference method. In the solution of the advection equation, Lagrange fifth, cubic spline, Hermite third and fifth interpolating polynomials were tested by numerical experiment and theoretical error analysis. Among these, Hermite interpolating polynomials are generally superior to Lagrange and cubic spline interpolating polynomials in reducing both dissipation and dispersion errors.

• Kyungpook Mathematical Journal
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• v.24 no.1
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• pp.55-61
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• 1984

• Communications of the Korean Mathematical Society
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• v.22 no.3
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• pp.475-485
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• 2007

We construct high-degree interpolation rules using not only pointwise values of a function but also of its derivatives up to the p-th order at equally spaced nodes on a closed and bounded interval of interest by introducing a linear functional from which we produce systems of linear equations. The linear systems will lead to a conclusion that the rules are uniquely determined for the nodes. An example is provided to compare the rules with the classical interpolating polynomials.

• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.383-387
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• 2002

Let p be an odd prime, and let f($\varkappa$) be the interpolating polynomial associated with a table of data points (j+1, (equation omitted) ) for 0$\leq$j$\leq$p. In this article, we find congruence identities modulo p of (p-1)!f($\varkappa$), (p-2)!f($\varkappa$), and (p-3)!f($\varkappa$). Moreover we present some conjectures of these types.

• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.397-407
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• 2006

We construct polynomial-fitting interpolation rules to agree with a function f and its first derivative f' at equally spaced nodes on the interval of interest by introducing a linear functional with which we produce systems of linear equations. We also introduce a matrix whose determinant is not zero. Such a property makes it possible to solve the linear systems and then leads to a conclusion that the rules are uniquely determined for the nodes. An example is investigated to compare the rules with Hermite interpolating polynomials.

• Nuclear Engineering and Technology
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• v.8 no.4
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• pp.209-217
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• 1976

A finite element method is formulated for one-speed integral equation it or the neutron transport in a slab reactor. The formulation incorporates both the linear and the cubic Hermite interpolating polynomials and is used to compute the approximate solutions for the slab criticality and Milne problem. The results are compared with the exact solutions available and then the effectiveness of the method is extensively discussed.

• Water for future
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• v.28 no.5
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• pp.151-162
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• 1995

A two-dimensional stream tube dispersion model is developed to simulate accurately transverse dispersion processes of pollutants in natural channels. Two distinct features of the stream tube dispersion model derived herein are that it employs the transverse cumulative discharge as an independent variable replacing the transverse distance and that it is developed in a natural coordinate system which follows the general direction of the channel flow. In the model studied, Eulerian-Lagrangian method is used to solve the stream tube dispersion equation. The stream tube dispersion equation is decoupled into two components by the operator-splitting approach; one is governing advection and the other is governing dispersion. The advection equation has been solved using the method of characteristics and the results are interpolated onto Eulerian grid on which the dispersion equation is solved by centered difference method. In solving the advection equation, cubic spline interpolating polynomials is used. In the present study, the results of the application of this model to a natural channel are compared with a steady-state flow measurements. Simulation results are in good accordance with measured data.