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## EXPLICIT ADAPTIVE TIMESTEPPING RUNGE-KUTTA INTEGRATORS
## (solvers/rkck54.py)
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## Milan Rother 2024
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# IMPORTS ==============================================================================
from ._rungekutta import ExplicitRungeKutta
# SOLVERS ==============================================================================
[docs]
class RKCK54(ExplicitRungeKutta):
"""Six-stage, 5th order explicit Runge-Kutta method by Cash and Karp.
Features an embedded 4th order method. The difference between the 5th and 4th order
results provides a 5th order error estimate, typically used to control the step size
while propagating the 5th order solution (local extrapolation). Known for good stability
properties compared to RKF45.
Characteristics:
* Order: 5 (Propagating solution)
* Embedded Order: 4
* Stages: 6
* Explicit
* Adaptive timestep
* Good stability, suitable for moderate accuracy requirements.
"""
def __init__(self, *solver_args, **solver_kwargs):
super().__init__(*solver_args, **solver_kwargs)
#number of stages in RK scheme
self.s = 6
#order of scheme and embedded method
self.n = 5
self.m = 4
#flag adaptive timestep solver
self.is_adaptive = True
#intermediate evaluation times
self.eval_stages = [0.0, 1/5, 3/10, 3/5, 1, 7/8]
#extended butcher table
self.BT = {
0: [ 1/5],
1: [ 3/40, 9/40],
2: [ 3/10, -9/10, 6/5],
3: [ -11/54, 5/2, -70/27, 35/27],
4: [1631/55296, 175/512, 575/13824, 44275/110592, 253/4096],
5: [ 37/378, 0, 250/621, 125/594, 0, 512/1771]
}
#coefficients for local truncation error estimate
self.TR = [-277/64512, 0, 6925/370944, -6925/202752, -277/14336, 277/7084]