Extended exponentially fitted interpolation formulas for oscillatory functions

摘要

We consider exponentially fitted interpolation formulas that use not only the pointwise values of an ω-dependent function f but also of its derivatives up to the nth order at the two boundary nodes of a closed interval [a,b]. The function f is of the form,f(x)=f1(x)cos(ωx)+f2(x)sin(ωx),x∈[a,b],where the functions f1 and f2 are smooth on the interval. As n increases, numerical results about the errors for the formulas are illustrated and compared. Some properties of the coefficients of the formulas at the two nodes are presented and extended to the case with three nodes. We investigate if the properties of the coefficients can be generalised to the cases with more than three nodes. Finally some other numerical results regarding the errors are given.