Frequency-dependent interpolation rules using first derivatives for oscillatory functions

We construct frequency-dependent rules to interpolate oscillatory functions y ( x ) with frequency ω of the form, y ( x ) = f 1 ( x ) cos ( ω x ) + f 2 ( x ) sin ( ω x ) , at equidistant nodes on the interval of interest where the functions f 1 and f 2 are smooth. Error analysis of the rules is investigated and numerical results are discussed. We provide numerical illustrations to compare the accuracy of classical Hermite polynomials and newly constructed frequency-dependent rules.