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## EXPLICIT STRONG STABILITY PRESERVING RUNGE-KUTTA INTEGRATOR
## (solvers/ssprk34.py)
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## Milan Rother 2024
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# IMPORTS ==============================================================================
from ._rungekutta import ExplicitRungeKutta
# SOLVERS ==============================================================================
[docs]
class SSPRK34(ExplicitRungeKutta):
"""Four-stage, 3rd order, Strong Stability Preserving (SSP) explicit Runge-Kutta method.
Provides a larger stability region compared to SSPRK33, particularly along the negative
real axis, at the cost of an additional stage. Useful when stability is more critical
than computational cost for a 3rd order explicit method.
Characteristics:
* Order: 3
* Stages: 4
* Explicit (SSP)
* Fixed timestep only
* Enhanced stability compared to SSPRK33.
"""
def __init__(self, *solver_args, **solver_kwargs):
super().__init__(*solver_args, **solver_kwargs)
#number of stages in RK scheme
self.s = 4
#order of scheme
self.n = 3
#intermediate evaluation times
self.eval_stages = [0.0, 1/2, 1, 1/2]
#butcher table
self.BT = {0:[1/2],
1:[1/2, 1/2],
2:[1/6, 1/6, 1/6],
3:[1/6, 1/6, 1/6, 1/2]}