Examples

Chaotic three-state ODE solved with DoPri5, plus uncertainty propagation across initial conditions.

• beginner

Hybrid system showing event detection at ground contact, with restitution-based velocity reset.

• beginner
• events
• dense output

Tour of every numra ODE solver, plus the auto-selection logic that picks the right one from problem hints.

• intermediate
• stiff
• dense output

Stiff ODE benchmark comparing explicit DoPri5 against implicit Radau5 across stiffness levels.

• intermediate
• stiff

Linear parabolic PDE solved by method of lines with Dirichlet boundaries.

• intermediate
• stiff

SDE option-pricing example with ensemble statistics across Euler-Maruyama, Milstein, and SRA1.

• intermediate

Classic chaotic delay differential equation solved by method of steps.

• intermediate

Pendulum solved both as an ODE in polar coordinates and as a DAE with a holonomic constraint.

• intermediate

Delay-parameter study showing the periodic → chaotic → hyperchaotic transition in Mackey-Glass.

• advanced

Caputo-derivative FDE solved by L1 scheme, with the Mittag-Leffler exact solution as reference.

• advanced

Integro-differential equation for stress relaxation, evaluated with O(1)-memory Prony recursion.

• advanced

One-phase melting/solidification PDE on a fixed domain via coordinate transformation.

• advanced
• stiff

Linear parabolic SPDE with additive space-time white noise; deterministic limit recovered as σ → 0.

• advanced
• stiff

Stochastic heat equation comparing fixed vs. adaptive time stepping; convergence to deterministic limit.

• advanced
• stiff