## Scientific Computing Workflow
Computation is the third pillar of science, turning complex real-world problems into trustworthy numerical answers.
| Pipeline Stage | Action & Purpose |
|---|---|
| 1. Model | Translate real systems into mathematics, often differential equations or optimization. |
| 2. Discretise | Replace continuous models with finite approximations (grids, finite unknowns). |
| 3. Solve | Apply root-finders, linear solvers, and time-stepping using vectorised libraries. |
| 4. Validate | Check against known cases, assessing error and stability via grid refinement. |
| 5. Interpret | Turn raw numbers into scientific understanding and visualisation. |
Every unit theme matters here: floating-point limits bound accuracy, stability decides trust, and vectorisation makes large problems feasible.
## The Validation Imperative
Numerical results are approximate and must be validated. A simulation produces numbers no matter what; the scientist's job is to know how accurate they are and where they might fail.
Common pitfall: treating a simulation's output as reliable truth without validation. A numerical model can be wrong from discretisation error, instability, ill-conditioning, or bugs.
The workflow requires a strict validation step. Checking against conservation laws and experiments transforms unverified code into a credible scientific result. Blind trust is as unscientific as a blank page.