Adaptive Hermite spectral methods in unbounded domains

A novel adaptive spectral method has been recently developed to numerically solve partial differential equations (PDEs) in unbounded domains. To achieve accuracy and improve efficiency, the relies on dynamic adjustment of three key tunable parameters: scaling factor, a displacement basis functions, expansion order. In this paper, we perform first numerical analysis using generalized Hermite functions both one- multi-dimensional problems. Our reveals why methods work well when “frequency indicator” solution is controlled. We then investigate how implementation affects results, thereby providing guidelines for proper tuning parameters. Finally, further performance by extending allow bidirectional function translation, prospect carrying out similar solving PDEs arising from realistic difficult-to-solve models with also briefly discussed.