Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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EXPONENTIALLY FITTED INTERPOLATION FORMULAS INVOLVING FIRST AND HIGHER-ORDER DERIVATIVES

  • Received : 2013.04.19
  • Accepted : 2013.06.05
  • Published : 2013.09.30
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Abstract

We construct exponentially fitted interpolation formulas using the values of the ${\omega}$-dependent function $f$ as well as its derivatives up to the $n$th order at a finite number of nodes on a closed interval ${\Omega}$. The function $f$ is of the form, $$f(x)=f_1(x)cos({\omega}x)+f_2(x)sin({\omega}x),x{\in}{\Omega}$$, where $f_1$ and $f_2$ are smooth enough to be approximated by polynomials on ${\Omega}$. Some properties of the formulas are newly found. The properties are numerically investigated and reexamined by producing some figures.

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References

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Cited by

  1. EXPONENTIALLY FITTED INTERPOLATION FORMULAS DEPENDING ON TWO FREQUENCIES vol.34, pp.3_4, 2016, https://doi.org/10.14317/jami.2016.207
  2. Extended exponentially fitted interpolation formulas for oscillatory functions vol.224, 2013, https://doi.org/10.1016/j.amc.2013.08.039