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##
## EMBEDDED DIAGONALLY IMPLICIT RUNGE KUTTA METHOD
## (solvers/esdirk32.py)
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## Milan Rother 2024
##
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# IMPORTS ==============================================================================
from ._rungekutta import DiagonallyImplicitRungeKutta
# SOLVERS ==============================================================================
[docs]
class ESDIRK32(DiagonallyImplicitRungeKutta):
"""Four-stage, 3rd order Embedded Singly Diagonally Implicit Runge-Kutta (ESDIRK) method.
Features an embedded 2nd order method for adaptive step size control. The first stage
is explicit (FSAL property not present in this specific implementation structure).
Designed to be applicable to index-2 Differential Algebraic Equations (DAEs).
FROM:
Williams et al.
Characteristics:
* Order: 3
* Embedded Order: 2
* Stages: 4 (1 Explicit, 3 Implicit)
* Implicit (ESDIRK)
* Adaptive timestep
* 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 and embedded method
self.n = 3
self.m = 2
#flag adaptive timestep solver
self.is_adaptive = True
#intermediate evaluation times
self.eval_stages = [0.0, 1.0, 3/2, 1.0]
#butcher table
self.BT = {
0: None, #explicit first stage
1: [1/2, 1/2],
2: [5/8, 3/8, 1/2],
3: [7/18, 1/3, -2/9, 1/2]
}
#coefficients for truncation error estimate
self.TR = [-1/9, -1/6, -2/9, 1/2]