Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2022; 37(1): 303-326

Online first article September 29, 2021      Printed January 31, 2022

https://doi.org/10.4134/CKMS.c210010

Copyright © The Korean Mathematical Society.

Hermite-type exponentially fitted interpolation formulas using three unequally spaced nodes

Kyung Joong Kim

Korea Aerospace University

Abstract

Our aim is to construct Hermite-type exponentially fitted interpolation formulas that use not only the pointwise values of an $omega$-dependent function $f$ but also the values of its first derivative at three unequally spaced nodes. The function $f$ is of the form, egin{equation*} egin{array}{ccc} f(x) = g_1(x) cos (omega x) + g_2(x) sin (omega x), ,, x in [a, b], end{array} end{equation*} where $g_1$ and $g_2$ are smooth enough to be well approximated by polynomials. To achieve such an aim, we first present Hermite-type exponentially fitted interpolation formulas $I_N$ built on the foundation using $N$ unequally spaced nodes. Then the coefficients of $I_N$ are determined by solving a linear system, and some of the properties of these coefficients are obtained. When $N$ is $2$ or $3,$ some results are obtained with respect to the determinant of the coefficient matrix of the linear system which is associated with $I_N.$ For $N=3,$ the errors for $I_N$ are approached theoretically and they are compared numerically with the errors for other interpolation formulas.

Keywords: Exponentially fitted, interpolation

MSC numbers: 65D05

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