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)$
* Re( h\cdot . 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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