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## DIAGONALLY IMPLICIT RUNGE KUTTA METHOD
## (solvers/dirk3.py)
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## Milan Rother 2024
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# IMPORTS ==============================================================================
from ._rungekutta import DiagonallyImplicitRungeKutta
# SOLVERS ==============================================================================
[docs]
class DIRK3(DiagonallyImplicitRungeKutta):
"""Four-stage, 3rd order, L-stable Diagonally Implicit Runge-Kutta (DIRK) method.
L-stability (A-stability and stiffly accurate, i.e., :math:`|R(\\infty)| = 0`) makes
this method suitable for stiff problems where damping of high-frequency components
is desired.
(Butcher tableau often attributed to Crouzeix, or Nørsett-Thomsen based on Wikipedia/Hairer).
Characteristics:
* Order: 3
* Stages: 4 (Implicit)
* Implicit (DIRK)
* Fixed timestep only
* L-stable (and thus A-stable)
"""
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 = [1/2, 2/3, 1/2, 1.0]
#butcher table
self.BT = {0:[1/2],
1:[1/6, 1/2],
2:[-1/2, 1/2, 1/2],
3:[3/2, -3/2, 1/2, 1/2]}