C1-collocation semidiscretization of ut + cux = 0: its fourier analysis and equivalence to the Galerkin method with linear splines

The Fourier analysis of C1-collocation semidiscretization at the Gauss points, for the hyperbolic equation ut + cux = 0, is performed by use of tridiagonal C1-collocation, i.e., a new 3-point finite difference reformulation of the method. The results are compared with Vichnevetsky's general 3-point family and Galerkin's B-spline semidiscretizations. Furthermore, it is shown that the C1-collocation method with spacing h (sampling frequency ω0) and the Galerkin method with linear splines and spacing 12h (sampling frequency 2ω0) produce the same numerical phase velocity and the same nodal approximations at both the common and the noncommon nodes.