Explanation of problems with Forward Euler

• $a\Delta t= 2\cdot 1.25=2.5$ and $A=-1.5$: oscillations and growth
• $a\Delta t = 2\cdot 0.75=1.5$ and $A=-0.5$: oscillations and decay
• $\Delta t=0.5$ and $A=0$: $u^n=0$ for $n>0$
• Smaller $Delta t$: qualitatively correct solution