Order of accuracy & Stability

This snippet shows how I examine the order of accuracy (OOA) and the numerical stability for a given numerical scheme.

In this snippet I examine the OOA and the stability for Lele's 6th-order numerical scheme [1] using a challeging stationary-wave problem proposed by Brady & Livescu (2019) [2] using the one-dimensional system of the wave equation.

Refs:

[1] Lele, Sanjiva K. "Compact finite difference schemes with spectral-like resolution." Journal of computational physics103.1 (1992): 16-42.

[2] Brady, Peter T., and Daniel Livescu. "High-order, stable, and conservative boundary schemes for central and compact finite differences." Computers & Fluids 183 (2019): 84-101.