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##
## EXPLICIT ADAPTIVE TIMESTEPPING RUNGE-KUTTA INTEGRATORS
## (solvers/rkf21.py)
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## Milan Rother 2025
##
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# IMPORTS ==============================================================================
from ._rungekutta import ExplicitRungeKutta
# SOLVERS ==============================================================================
[docs]
class RKF21(ExplicitRungeKutta):
"""3-stage 2-nd order embedded Runge-Kutta-Fehlberg method
with 2-nd order truncation error estimate that can be used to
adaptively control the timestep.
This is an absolute classic, the three stages make it relatively
cheap, but its only second order and the error estimate is not that
accurate. However, if you need some kind of adaptive integrator, and
the timestep is not limited by the local truncation error, this solver
might be a good choice.
"""
def __init__(self, *solver_args, **solver_kwargs):
super().__init__(*solver_args, **solver_kwargs)
#number of stages in RK scheme
self.s = 3
#order of scheme and embedded method
self.n = 2
self.m = 1
#flag adaptive timestep solver
self.is_adaptive = True
#intermediate evaluation times
self.eval_stages = [0.0, 1/2, 1]
#extended butcher table
self.BT = {
0: [ 1/2],
1: [1/256, 255/256],
2: [1/512, 255/256, 1/512]
}
#coefficients for local truncation error estimate
self.TR = [1/512, 0, -1/512]