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?