from simframe.integration.scheme import Scheme
# Butcher coefficients
a10 = 2/3
b0, b1 = 1/4, 3/4
c1 = 2/3
def _f_expl_2_ralston(x0, Y0, dx, *args, dYdx=None, **kwargs):
"""Explicit 2nd-order Ralston's 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
2/3 | 2/3 0
-----|---------
| 1/4 3/4
"""
k0 = Y0.derivative(x0, Y0) if dYdx is None else dYdx
k1 = Y0.derivative(x0 + c1*dx, Y0 + a10*k0*dx)
return dx*(b0*k0 + b1*k1)
[docs]
class expl_2_ralston(Scheme):
"""Class for explicit 2nd-order Ralston's method"""
def __init__(self, *args, **kwargs):
super().__init__(_f_expl_2_ralston,
description="Explicit 2nd-order Ralston's method", *args, **kwargs)