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}
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