braincell.quad.euler_step

Contents

braincell.quad.euler_step#

braincell.quad.euler_step(target, *args)[source]#

Advance one step with the explicit (forward) Euler method.

Forward Euler is the simplest explicit Runge-Kutta scheme. For a system

\[\frac{dy}{dt} = f(t, y),\]

the update reads

\[y_{n+1} = y_n + \Delta t \, f(t_n, y_n).\]

The local truncation error is \(O(\Delta t^2)\) and the global error is \(O(\Delta t)\) (first-order accurate). The method is only conditionally stable; for stiff problems prefer backward_euler_step(), exp_euler_step(), or one of the implicit Runge-Kutta variants.

Parameters:

  • target (DiffEqModule) – Differential-equation module to advance. Its pre_integral(), compute_derivative(), and post_integral() hooks are called by the underlying Runge-Kutta driver.

  • *args – Extra positional arguments forwarded to target’s pre/derivative/post hooks (typically the input currents for this step).

Returns:

The state held inside target (every DiffEqState) is updated in place.

Return type:

None

See also

midpoint_step, rk2_step, heun2_step

rk4_step

Classical fourth-order Runge-Kutta.

backward_euler_step

Implicit (backward) Euler counterpart.

Notes

The corresponding Butcher tableau (stored as euler_tableau) is

\[\begin{split}\begin{array}{c|c} 0 & 0 \\ \hline & 1 \end{array}.\end{split}\]

The current time t and step size dt are read from the active brainstate.environ context.

Examples

>>> import brainstate
>>> import brainunit as u
>>> from braincell.quad import euler_step
>>> with brainstate.environ.context(t=0. * u.ms, dt=0.01 * u.ms):
...     euler_step(my_neuron)
Contents