Tridiagonal C1-collocation

It is shown that one-dimensional C1-collocation at the Gauss points may be viewed as a member of a family of 3-point finite difference schemes. This new formulation of the method leads to a simple practical technique for the elimination of the derivative degrees of freedom. In contrast to what is known about standard collocation matrices, the new matrix has all the desirable features, exactly as the matrices of other popular methods do: it is tridiagonal and, depending on the nature of the differential operator, it can be Toeplitz, (strictly) diagonally dominant, symmetric or positive definite.