braincell.quad.implicit_rk4_step

braincell.quad.implicit_rk4_step#

braincell.quad.implicit_rk4_step(target, t, dt, *args)[source]#

Advance a cell with implicit Euler voltage and explicit RK4 channels.

Operator-splitting update inside one dt for a multi-compartment cell:

  1. Channels and concentrations. With axial currents temporarily disabled, every non-voltage DiffEqState is advanced by rk4_step().

  2. Cable voltage. The linear axial system \(dV/dt = A V\) is then advanced by one implicit-Euler solve via _implicit_euler_for_axial_current(), \((I - \Delta t A) V_{n+1} = V_n\).

For non-Cell targets the routine falls back to a single Newton-based implicit Euler step on the full state vector.

The implicit Euler voltage solve is \(L\)-stable and damps high-frequency cable modes; the explicit RK4 channel update gives the rest of the system fourth-order accuracy. Use this scheme when the cable equation is the only severely stiff component and you want extra accuracy on smooth gating dynamics.

Parameters:

  • target (DiffEqModule) – The module to advance. Splitting is used when target is a braincell.Cell; otherwise the routine reduces to a plain Newton step.

  • t (Quantity[s]) – Current simulation time.

  • dt (Quantity[s]) – Time step.

  • *args – Extra positional arguments forwarded to the channel and voltage solvers.

Returns:

target’s state is updated in place.

Return type:

None

See also

cn_rk4_step

Crank-Nicolson voltage solve paired with RK4 channels.

implicit_exp_euler_step

Implicit Euler voltage solve paired with exponential Euler channels.