from simframe.integration.scheme import Scheme
# Butcher coefficients
a10 = 1/2
a21 = 1/2
b0, b1, b2, b3 = 1/6, 1/3, 1/3, 1/6
c1, c2 = 1/2, 1/2
def _f_expl_4_runge_kutta(x0, Y0, dx, *args, dYdx=None, **kwargs):
"""Explicit 4th-order classical Runge-Kutta method
Parameters
----------
x0 : Intvar
Integration variable at beginning of scheme
Y0 : Field
Variable to be integrated at the beginning of scheme
dx : IntVar
Stepsize of integration variable
dYdx : Field, optional, default : None
Current derivative. Will be calculated, if not set.
args : additional positional arguments
kwargs : additional keyworda arguments
Returns
-------
dY : Field
Delta of variable to be integrated
Butcher tableau
---------------
0 | 0 0 0 0
1/2 | 1/2 0 0 0
1/2 | 0 1/2 0 0
1 | 0 0 1 0
-----|-----------------
| 1/6 1/3 1/3 1/6
"""
k0 = Y0.derivative(x0, Y0) if dYdx is None else dYdx
k1 = Y0.derivative(x0 + c1*dx, Y0 + a10*k0*dx)
k2 = Y0.derivative(x0 + c2*dx, Y0 + a21*k1*dx)
k3 = Y0.derivative(x0 + dx, Y0 + k2*dx)
return dx*(b0*k0 + b1*k1 + b2*k2 + b3*k3)
[docs]
class expl_4_runge_kutta(Scheme):
"""Class for explicit 4th-order classical Runge-Kutta method"""
def __init__(self, *args, **kwargs):
super().__init__(_f_expl_4_runge_kutta,
description="Explicit 4th-order classical Runge-Kutta method", *args, **kwargs)