Week 5 - Literature review: ODE Stability

When does an ODE become unstable?

When the discretization points are too less while discretizing an ODE over a domain, the ODE may become unstable

For a time marching solution, the explicit scheme leads to instability when the discrete time steps is large

How does stability affect engineering simulations?

In engineering simulations, instability leads to incorrect results. A good numerical scheme used to solve ODEs should converge the solution towards the true analytical value at every time step. The instability leads to divergence of the solution from the true value. This instability may also lead to unrealistic and non-physical results

Can stability condition be derived for all types of problems?

Stability conditions can be derived for all types of problems. There are two common stability condition they are

1.Eigen Value stability condition.

2.Von Neuman stability condition