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##
## EXPLICIT STRONG STABILITY PRESERVING RUNGE-KUTTA INTEGRATOR
## (solvers/ssprk33.py)
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## Milan Rother 2024
##
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# IMPORTS ==============================================================================
from ._rungekutta import ExplicitRungeKutta
# SOLVERS ==============================================================================
[docs]
class SSPRK33(ExplicitRungeKutta):
"""Three-stage, 3rd order, Strong Stability Preserving (SSP) explicit
Runge-Kutta method.
Offers higher accuracy than SSPRK22 while maintaining the SSP property.
A popular choice for problems where TVD properties are important or when
a simple, stable 3rd order explicit method is needed.
Characteristics:
* Order: 3
* Stages: 3
* Explicit (SSP)
* Fixed timestep only
* Good stability properties for an explicit 3rd order method.
"""
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
self.n = 3
#intermediate evaluation times
self.eval_stages = [0.0, 1.0, 0.5]
#butcher table
self.BT = {0:[1.0],
1:[1/4, 1/4],
2:[1/6, 1/6, 2/3]}
[docs]
def interpolate(self, r, dt):
k1, k2, k3 = self.K[0], self.K[1], self.K[2]
b1, b2, b3 = r*(2-r)**2/2, r**2*(3-2*r)/2, r**3
return self.x_0 + dt*(b1 * k1 + b2 * k2 + b3 * k3)