Summary - Things good to know by heart

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• Stability: solution goes -> 0
• Residual for step methods: Taylor expand the formula and see what order the RHS is.
Stability region for y' = f(y,t). Derive by expanding for a perturbation y s.t.: 

$$f(y,t)=ky$$

, put in the method and 
• $Re(hf(y))<0$ for trapetzoid
• |1+ hf| < 1 for Explicit euler
• |1- hf| > 1 for implicit euler
• Method of lines: Solve a PDE as a system of ODEs
•  {Elliptic, parabolic, hyperbolic} equations: B^2 - A C {<0, = 0 or > 0}