Cubic Polynomial Interpolation Research Articles

Fractional Age Assumption Based on Cubic Polynomial Interpolation

This article proposes a new fractional age assumption (FAA) based on the cubic polynomial interpolation (CPI) and applies it to estimate the mortality rate and related actuarial quantities. The validity of the method under CPI is proved theoretically and the valuable advantages of CPI assumption are discussed based on three different perspectives—utilized death information, property of mortality force, and optimality criterion. The results show that CPI assumption has distinct valuable superiority compared with other FAAs in references. Finally under CPI assumption we study the calculations of some important actuarial quantities in life contingencies.

High Order Cubic-Polynomial Interpolation Schemes on Triangular Meshes

Abstract The Cubic-Polynomial Interpolation scheme has been developed and applied to many practical simulations. However, it seems the existing Cubic-Polynomial Interpolation scheme are restricted to uniform rectangular meshes. Consequently, this scheme has some limitations to problems in irregular domains. This paper will extend the Cubic-Polynomial Interpolation scheme to triangular meshes by using some spline interpolation techniques. Numerical examples are provided to demonstrate the accuracy of the proposed schemes.

Valence state map of iron oxide thin film obtained from electron spectroscopy imaging series

This paper demonstrates the applicability of electron-spectroscopic imaging (ESI) for valence-state mapping of the iron oxide system. We have previously developed a set of signal-processing methods for an ESI series, to allow mapping of sp 2/sp 3 ratio, dielectric function and energy bandgap. In this study, these methods are applied to generate a valence-state map of an iron oxide thin film (Fe/α-Fe 2O 3). Two problems, data undersampling and a convolution effect associated with extraction of the image-spectrum from the core loss image series, were overcome by using cubic-polynomial interpolation and maximum-entropy deconvolution. As a result, the reconstructed image-spectrum obtained from the ESI series images has a quality as good as that of conventional electron energy-loss spectra. The L 3/ L 2 ratio of the reconstructed ESI spectrum is determined to be 3.30 ± 0.30 and 5.0 ± 0.30 for Fe and α-Fe 2O 3, respectively. Our L 3/ L 2 ratio mapping shows an accurate correspondence across the Cu/Fe/α-Fe 2O 3 region. The effect of delocalization and chromatic aberration on the ESI resolution is discussed and estimated to be about 2 nm for the case of L 3/ L 2 ratio mapping.

Comparisons of CIP, compact and CIP‐CSL2 schemes for reproducing internal solitary waves

AbstractSix different models were evaluated for reproducing internal solitary waves which occur and propagate in a stratified flow field with a sharp interface. Three stages were used to compute internal solitary waves in a stratified field: (1) first‐phase computation of momentum equations, (2) second‐phase computation of momentum equations, which corresponds to computing the Poisson's equation, and (3) density computation. The six models discussed in this paper consisted of combinations of four different schemes, a three‐point combined compact difference scheme (CCD), a normal central difference scheme (CDS), a cubic‐polynomial interpolation (CIP), and an exactly conservative semi‐Lagrangian scheme (CIP‐CSL2). The residual cutting method was used to solve the Poisson's equation. Three tests were used to confirm the validity of the computations using KdV theory; i.e. the incremental wave speed and amplitude of internal solitary waves, the maximum horizontal velocity and amplitude, and the wave form. In terms of the shape of an internal solitary wave, using CIP for momentum equations was found to provide better performance than CCD. These results suggest one of the most appropriate scheme for reproducing internal solitary waves may be one in which CIP is used for momentum equations and CCD to solve the Poisson's equation. Copyright © 2005 John Wiley & Sons, Ltd.

The Harmonic Constant Datum Method: Options for Overcoming Datum Discontinuities at Mixed–Diurnal Tidal Transitions*

Abstract The harmonic constant datum (HCD) method is a computationally efficient way of estimating tidal datums relative to mean sea level, without the need to compute long time series. However, datum discontinuities can occur between mixed and diurnal tidal regimes using this method. Solutions to this problem are investigated, with a hypothetical strait that contains a semidiurnal node, using three different procedures: algorithms specifically designed for diurnal tides (DTA), mixed tidal algorithms (MTA) throughout, and cubic polynomial interpolation (CPI) across the diurnal region. DTA creates small discontinuities (≤11% for the strait) in mean higher high water and mean lower low water but does not provide estimates of mean high water or mean low water. MTA gives continuous datums but creates artificial structures in the middle of the diurnal region. CPI provides smooth, continuous datums but does not use the tidal information within the diurnal regions. Which procedure works best depends on the size ...

Numerical simulation by cubic-polynomial interpolation for unsteady, incompressible, viscous flow

Tuncer, I. H., Ekaterinaris, J. A., and Platzer, M. R, A Viscous-Inviscid Interaction Method for 2-D Unsteady, Compressible Flows, AIAA Paper 93-3019, June 1993. Tuncer, I. H., Ekaterinaris, J. A., and Platzer, M. E, A Novel ViscousInviscid Interaction Method with Inviscid Wake Modeling, AIAA Paper 94-0178, Jan. 1994. Ekaterinaris, J. A., Cricelli, A., and Platzer, M. E, A Zonal Method for Unsteady, Viscous, Compressible Airfoil Flows, Journal of Fluids and Structures, Vol. 8, Jan. 1994, pp. 107-123. McAlister, K. W., Pucci, S. L., McCroskey, W. J., and Carr, L. W., An Experimental Study of Dynamic Stall on Advanced Airfoil Sections, Pressure and Force Data, Vol. 2, NASA-TM-84245, Sept. 1982.

A universal solver for hyperbolic equations by cubic-polynomial interpolation I. One-dimensional solver

A new numerical method is proposed for general hyperbolic equations. The scheme uses a spatial profile interpolated with a cubic polynomial within a grid cell, and is described in an explicit finite-difference form by assuming that both a physical quantity and its spatial derivative obey the master equation. The method gives stable and less diffusive results even without any flux limiter. It is successfully applied to the KdV equation, a one-dimensional shock-tube problem and a cylindrically converging shock wave.

A universal solver for hyperbolic equations by cubic-polynomial interpolation II. Two- and three-dimensional solvers

A new numerical method is proposed for multidimensional hyperbolic equations. The scheme uses a cubic spatial profile within grids, and is described in an explicit finite-difference form by assuming that both the physical quantity and its spatial derivative obey the master equation. The method gives a stable and less diffusive result than the old methods without any flux limiter. Extension to nonlinear equations with nonadvection terms is straightforward.

Cubic interpolated pseudo-particle method (CIP) for solving hyperbolic-type equations

Abstract A new cubic-polynomial interpolation method, where the gradient of the quantity is a free parameter, is proposed for solving hyperbolic-type equations. Various choices of the gradient are investigated, and a stable and less diffusive scheme is made possible without the clipping or the flux-correction procedure.