Frequency-dependent interpolation rules using first derivatives for oscillatory functions

We construct frequency-dependent rules to interpolate oscillatory functions y(x)y(x) with frequency ωω of the form,y(x)=f1(x)cos(ωx)+f2(x)sin(ωx),y(x)=f1(x)cos(ωx)+f2(x)sin(ωx),at equidistant nodes on the interval of interest where the functions f1f1 and f2f2 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.