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http://dx.doi.org/10.14317/jami.2013.677

EXPONENTIALLY FITTED INTERPOLATION FORMULAS INVOLVING FIRST AND HIGHER-ORDER DERIVATIVES  

Kim, Kyung Joong (School of Liberal Arts and Sciences, Korea Aerospace University)
Publication Information
Journal of applied mathematics & informatics / v.31, no.5_6, 2013 , pp. 677-693 More about this Journal
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.
Keywords
Exponentially fitted; Interpolation;
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