HERMITE-TYPE EXPONENTIALLY FITTED INTERPOLATION FORMULAS USING THREE UNEQUALLY SPACED NODES

Our aim is to construct Hermite-type exponentially fitted interpolation formulas that use not only the pointwise values of an omega-dependent function f but also the values of its first derivative at three unequally spaced nodes. The function f is of the form, f (x) = g(1)(x) cos(omega x) + g(2)(x) sin(omega x), x is an element of [a, b], where g(1) and g(2) are smooth enough to be well approximated by polynomials. To achieve such an aim, we first present Hermite-type exponentially fitted interpolation formulas I-N built on the foundation using N unequally spaced nodes. Then the coefficients of I-N are determined by solving a linear system, and some of the properties of these coefficients are obtained. When N is 2 or 3, some results are obtained with respect to the determinant of the coefficient matrix of the linear system which is associated with I-N. For N = 3, the errors for I-N are approached the-oretically and they are compared numerically with the errors for other interpolation formulas.