Differential equations and optimisation
These operations return not a formula but a numerical result. The How? panel then states exactly which algorithm ran, with which settings — which is not a detail: two methods can answer the same problem differently.
Differential equations
“≡ Selection” ▸ Operation ▸ Models ▸ Differential equation. You write the system, the initial conditions, the time interval. The solver is SciPy's; the method (adaptive Runge-Kutta, or an implicit method for a stiff problem) is chosen according to the system and displayed.
The output includes the trajectory, and for a two-variable system the phase portrait — the trajectory in the plane of the two unknowns, which shows at a glance whether there is a cycle, an equilibrium point or a divergence.
Roots and optimisation
- Roots of an equation — for an equation symbolic computation cannot solve in closed form. Give an interval or a starting point.
- Optimisation — minimise or maximise a function, with or without constraints. The method used and the number of iterations are stated.
A calculation that runs long makes “⏹ Stop” appear next to “Compute”. The stop is real, not cosmetic; if the engine has to be rebuilt, the document replays its variables on its own and tells you so.
Try it: the “SIR epidemic” template
“From a template” ▸ SIR epidemic: three coupled equations, solved over a year, from which come R₀, the date of the peak, the final size of the epidemic and the herd-immunity threshold. Change the contact rate and watch the peak move. The Reaction of unknown order template shows the other use: three models fitted, the one that lines up best wins.
Where to go next
To plot other than by default — 3D surface, vector field — use the Visualisation operation in the same menu. For a solver the application does not offer, the Python cell gives direct access to SciPy.