Stability and accuracy of the Cubic Interpolated Propagation scheme

We have studied the stability and accuracy of the advection phase calculation of the Cubic Interpolated Propagation scheme, which solves the universal hyperbolic equation. An advection equation with a constant velocity field is examined using Fourier analysis. The results show that the scheme is stable, the group velocity is almost constant, and the gain is near unity for a wide range of wave numbers. The low dissipation and dispersion of the scheme result from an approximation that uses nodal values of both physical quantities and their spatial derivatives.