MirankerLinigerP.py

import numpy as np

def mirankerLinigerP(f, tspan, y0, N):
    """
    Solves ODEs using a parallel predictor-corrector method.

    This function solves the differential equation dy/dt = f(t, y) with
    an initial value y0 over the time interval specified by tspan,
    using N steps of a parallel predictor-corrector method.

    Parameters
    ----------
    f : callable
        Right-hand side of the ODE, f(t, y).
    tspan : tuple
        Time interval (start, end).
    y0 : array
        Initial value.
    N : int
        Number of time steps.

    Returns
    -------
    t : array
        Time points.
    y : array
        Solution values at time points.
    """
    # Time step
    dt = (tspan[1] - tspan[0]) / N
    t = np.linspace(tspan[0], tspan[1], N+1)

    # Initialize solution array
    y = np.zeros((len(y0), N+1))
    y[:, 0] = y0

    # Start with an Euler step
    y[:, 1] = y[:, 0] + dt * f(t[0], y[:, 0])
    yp = y[:, 1]

    # Parallel predictor-corrector method
    for n in range(2, N):
        # Parallel predictor step
        y[:, n] = y[:, n-1] + dt / 2 * (f(t[n], yp) + f(t[n-1], y[:, n-1]))

        # Corrector step
        yp = y[:, n-1] + 2 * dt * f(t[n], yp)

    return t, y