Question

What is the condition of stability for the forward Euler method when the function is real?

(a) \(\Delta t\frac{\partial f}{\partial\phi} <2\)

(b) \(\big|\Delta t\frac{\partial f}{\partial\phi}\big|<2\)

(c) Always stable

(d) Never statble

I got this question during a job interview.

Origin of the question is Transient Flows in portion Transient Flows of Computational Fluid Dynamics

Answer 1

Right choice is (b) \(\big|\Delta t\frac{\partial f}{\partial\phi}\big|<2\)

To explain: The forward Euler method is conditionally stable. For this method to be stable, it needs the following condition to be satisfied.

\(\big|1+\Delta t\frac{\partial f}{\partial\phi} \big|<1\)

When the function f is real, this becomes

\(\big|\Delta t\frac{\partial f}{\partial\phi} \big|<2\).