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https://codeberg.org/Yael-II/MSc2-Project-Chaos.git
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88 lines
2.4 KiB
Python
88 lines
2.4 KiB
Python
import numpy as np
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def euler(x0, y0, h, n, func): # FIXME cannot be used with vectors
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"""
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Euler method adapted for state vector [[x, y], [u, v]]
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:param x0: initial time value
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:param y0: initial state vector [[x, y], [u, v]]
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:param h: step size (time step)
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:param n: number of steps
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:param func: RHS of differential equation
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:returns: x array, solution array
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"""
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x_values = np.zeros(n)
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y_values = np.zeros((n, 2, 2)) # to accommodate the state vector
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for i in range(n):
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dydt = func(x0, y0)
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y0 = y0 + h * dydt
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x0 = x0 + h
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x_values[i] = x0
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y_values[i, :, :] = y0
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return x_values, y_values
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# Updated RK2 integrator
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def rk2(x0, y0, h, n, func): # FIXME cannot be used with vectors
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"""
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RK2 method adapted for state vector [[x, y], [u, v]]
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:param x0: initial time value
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:param y0: initial state vector [[x, y], [u, v]]
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:param h: step size (time step)
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:param n: number of steps
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:param func: RHS of differential equation
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:returns: x array, solution array
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"""
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x_values = np.zeros(n)
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y_values = np.zeros((n, 2, 2)) # to accommodate the state vector
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for i in range(n):
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k1 = func(x0, y0)
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k2 = func(x0 + h / 2., y0 + h / 2. * k1)
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y0 = y0 + h * (k1 / 2. + k2 / 2.)
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x0 = x0 + h
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x_values[i] = x0
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y_values[i, :, :] = y0
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return x_values, y_values
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def rk4(t0: float,
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W0: np.ndarray,
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h: float,
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n: int,
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func):
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"""
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RK4 method adapted for state vector [[x, y], [u, v]]
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:param x0: initial time value
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:param y0: initial state vector [[x, y], [u, v]]
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:param h: step size (time step)
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:param n: number of steps
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:param func: RHS of differential equation
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:returns: x array, solution array
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"""
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time = np.zeros(n)
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W = np.zeros((n,) + np.shape(W0))
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# to accommodate the state vector
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t = t0
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w = W0
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for i in range(n):
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k1 = func(t, w)
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k2 = func(t + h / 2., w + h / 2. * k1)
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k3 = func(t + h / 2., w + h / 2. * k2)
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k4 = func(t + h, w + h * k3)
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w = w + h * (k1 / 6. + k2 / 3. + k3 / 3. + k4 / 6.)
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t = t + h
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time[i] = t
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W[i] = w
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return t, W
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def integrator_type(x0, y0, h, n, func, int_type):
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return int_type(x0, y0, h, n, func)
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