Integrators#

Inspectable Euler, RK4 and adaptive integration of SI state models.

class engineeringkit.integrators.IntegrationResult(t, history, method, evaluations)[source]#

Bases: object

Output of engineeringkit.integrators.integrate_ode().

Parameters:

  • t (ndarray)

  • history (ndarray)

  • method (str)

  • evaluations (int)

evaluations: int#

Number of calls to the right-hand side.

Type:

int

history: ndarray#

State at each sample, shape (samples, states), in the model’s units.

Type:

ndarray

method: str#

Integration method used ("euler", "rk4" or a SciPy method name).

Type:

str

plot(labels=None, ax=None)[source]#

Plot each state against time; return (fig, ax).

Parameters:

  • labels (sequence of str, optional) – One label per state, including its unit (e.g. "x [m]").

  • ax (matplotlib.axes.Axes, optional) – Axes to draw on; a new figure is created if omitted.

Returns:

(fig, ax).

Return type:

tuple

summary()[source]#

Method, sample count, right-hand-side evaluations and final state.

Return type:

dict

t: ndarray#

Sample times [s], strictly increasing.

Type:

ndarray

engineeringkit.integrators.integrate_ode(rhs, y0, t, method='RK45', *, rtol=1e-08, atol=1e-10)[source]#

Solve \(dy/dt = f(t, y)\) on a strictly increasing finite time grid.

Parameters:

  • rhs (Callable) – rhs(t, y) returning the derivative, a finite array shaped like y0, in state units per second.

  • y0 (float or array_like) – Initial state, in the model’s units.

  • t (array_like) – At least two finite, strictly increasing sample times [s].

  • method (str) – "euler" or "rk4" for explicit fixed steps on the grid t; any other name is passed to scipy.integrate.solve_ivp() (e.g. "RK45", "Radau").

  • rtol (float) – Positive relative and absolute tolerances of the adaptive methods.

  • atol (float) – Positive relative and absolute tolerances of the adaptive methods.

Returns:

Times [s], the state history at each time and the number of right-hand-side evaluations.

Return type:

IntegrationResult

Raises:

  • ValueError – If the grid, initial state or tolerances are invalid, or rhs returns a nonfinite or wrongly shaped derivative.

  • RuntimeError – If a fixed-step state becomes nonfinite or the adaptive solver fails.

Notes

Explicit methods are for non-stiff teaching problems; the step size controls their stability and accuracy. Inputs are raw SI numbers with no dimensional metadata; see Numerical methods and inspectable histories.