Stability of numerical schemes#

In the previous chapter we analyzed the linear advection equation and its discretized version and we found that the solution could:

  • Remain bounded or not.

  • If it remained bounded, it could converge to the solution of the exact equation or not.

These behaviours are deeply related to the concept of numerical stability of the underlying numerical scheme used to discretize the equation. Moreover, they are common to every numerical scheme, so it is advantageous to devise a general methodology applicable to all numerical schemes.