= Scientific computing
<Scientific computing> turns scientific models into reproducible calculations through numerical and symbolic <algorithms>, with explicit attention to error and computational cost. The task includes selecting a model representation, solving the resulting equations and checking which features survive controlled changes in resolution or precision.
For a one-dimensional heat equation solved by explicit finite differences over a fixed physical time, halving the spatial grid spacing doubles the number of unknowns and typically requires four times as many time steps for stability. With linear work per step, the cost grows by about a factor of eight. This connects a physical resolution choice with an algorithmic resource requirement rather than treating finer resolution as free.
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