Stability and dispersion analysis of DFDM for the scalar wave equation

Summary This study investigates a particular instantiation of the distributional finite-difference method (DFDM) based on B-splines in the context of solving the 1D scalar wave equation, focusing on two key numerical properties: stability and numerical dispersion. By comparing DFDM against finite-difference and spectral-element methods, we assess the trade-offs between time step restrictions and accuracy. We introduce a cost metric to quantify the computational effort required to achieve a target dispersion error threshold. The results show that, while DFDM has more restrictive stability bounds, it offers superior dispersion performance at lower points per wavelength, making it particularly attractive for applications with tight memory requirements.