Numerics

[Any computer simulation will necessarily have finite accuracy.]

Stability

[Error is inevitable, too. A finite computer can have only finite accuracy. That is, it cannot be completely accurate and error-free. In many cases, such error will grow uncontrollably. ]

Constraints

[We can find an energy constraint in the problem of the falling apple.]

Gauge Conditions

[The "Pythagorean Theorem" for skewed, stretched grids is much more complicated than the one for Cartesian grids. Einstein's equations lead to a natural skewing, stretching, and worse.]

Boundary Conditions

[If we watch a wave move across water, and hit a wall—like in a bathtub or a pool—we'll see it reflect. If the wave runs up against a gently sloping shoreline, we won't see nearly as much reflection. It is inevitable that there will be edges in a numerical simulation. Whether those edges act like walls or like gentle shorelines is a very delicate issue. It depends on our numerics, and on our equations.]