beam_calculation.integrators.rk4 module

Define Runge-Kutta integraiton function.

rk4(u: ndarray, du: Callable[[float, ndarray], ndarray], x: float, dx: float) → ndarray

Compute variation of u between x and x+dx.

Use 4-th order Runge-Kutta method.

Note

This is a slightly modified version of the RK. The k_i are proportional to delta_u instead of du_dz.

Parameters:

• u (np.ndarray) – Holds the value of the function to integrate in x.

• du_dx (Callable[[float, np.ndarray], np.ndarray]) – Gives the variation of u components with x.

• x (float) – Where u is known.

• dx (float) – Integration step.

Returns:

delta_u – Variation of u between x and x+dx.

Return type:

np.ndarray