Stability, Consistency, Stiffness

• What is the definitition of stability for a finite difference representation of an ODE?
• For the linear ODE $y^\prime = -\alpha y+F(t)$, what is the maximum step size for Explicit Euler?
  • What about Implicit Euler?
• For a system of linear ODEs $dy/dt = F(y)$, where $y$ and $F$ are vectors, what is the maximum step size?
  • Show how this maximum step size is computed.
• For an ODE, what do we mean by consistency?
• What is a modified differential equation? How is it found?
• Give a working definition for a stiff ODE.
  • What is the general rule for methods applied to stiff ODEs?
• Give an example of a stiff ODE or ODE system.
• What is a QSSA and how does it relate to stiff systems?