A frequency-dependent p-adaptive technique for spectral methods

When using spectral methods, a consistent method for tuning the expansion order is often required, especially time-dependent problems in which oscillations emerge solution. In this paper, we propose frequency-dependent p-adaptive technique that adaptively adjusts based on frequency indicator. Using technique, combined with recently proposed scaling and moving techniques, are able to devise an adaptive unbounded domains can capture handle diffusion, advection, oscillations. As application, use numerically solve Schrödinger's equation domain successfully solution's oscillatory behavior at infinity.