Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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HERMITE-TYPE EXPONENTIALLY FITTED INTERPOLATION FORMULAS USING THREE UNEQUALLY SPACED NODES

  • Kim, Kyung Joong (School of Liberal Arts and Sciences Korea Aerospace University)
  • Received : 2021.01.08
  • Accepted : 2021.08.13
  • Published : 2022.01.31
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Abstract

Our aim is to construct Hermite-type exponentially fitted interpolation formulas that use not only the pointwise values of an 𝜔-dependent function f but also the values of its first derivative at three unequally spaced nodes. The function f is of the form, f(x) = g1(x) cos(𝜔x) + g2(x) sin(𝜔x), x ∈ [a, b], where g1 and g2 are smooth enough to be well approximated by polynomials. To achieve such an aim, we first present Hermite-type exponentially fitted interpolation formulas IN built on the foundation using N unequally spaced nodes. Then the coefficients of IN 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 IN. For N = 3, the errors for IN are approached theoretically and they are compared numerically with the errors for other interpolation formulas.

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