from simframe.integration.scheme import Scheme
# Butcher coefficients
a20, a21 = 1/4, 1/4
b0, b1, b2 = 1/6, 1/6, 2/3
c2 = 1/2
def _f_expl_3_ssprk(x0, Y0, dx, *args, dYdx=None, **kwargs):
"""Explicit 3rd-order Strong Stability Preserving 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
1 | 1 0 0
1/2 | 1/4 1/4 0
-----|-------------
| 1/6 1/6 2/3
"""
k0 = Y0.derivative(x0, Y0) if dYdx is None else dYdx
k1 = Y0.derivative(x0 + dx, Y0 + k0 * dx)
k2 = Y0.derivative(x0 + c2*dx, Y0 + (a20*k0 + a21*k1)*dx)
return dx*(b0*k0 + b1*k1 + b2*k2)
[docs]
class expl_3_ssprk(Scheme):
"""Class for explicit 3rd-order Strong Stability Preserving Runge-Kutta method"""
def __init__(self, *args, **kwargs):
super().__init__(_f_expl_3_ssprk,
description="Explicit 3rd-order Strong Stability Preserving Runge-Kutta method", *args, **kwargs)