ERK tableau registry

ERK_TABLEAU_REGISTRY maps human-friendly identifiers to ERKTableau instances. The registry powers get_algorithm_step() aliases and allows callers to select well-known explicit Runge–Kutta schemes without manually specifying the coefficients.

cubie.integrators.algorithms.ERK_TABLEAU_REGISTRY Dict[str, ERKTableau]

dict() -> new empty dictionary dict(mapping) -> new dictionary initialized from a mapping object’s

(key, value) pairs

dict(iterable) -> new dictionary initialized as if via:: d = {} for k, v in iterable:

d[k] = v
dict(**kwargs) -> new dictionary initialized with the name=value pairs: in the keyword argument list. For example: dict(one=1, two=2)

The default ERKStep configuration uses cubie.integrators.algorithms.generic_erk.DEFAULT_ERK_TABLEAU, the Dormand–Prince 5(4) pair. The "dopri54" alias mirrors the longer "dormand-prince-54" key so existing controller presets continue to work.

Available aliases

Named explicit Runge–Kutta tableaus
Key	Description	Reference
`"heun-21"`	Heun’s improved Euler method (order 2).	[Heun1900]
`"ralston-33"`	Ralston’s third-order method with minimized error constants.	[Ralston1962]
`"bogacki-shampine-32"`	Bogacki–Shampine embedded 3(2) pair with FSAL property.	[BogackiShampine1993]
`"dormand-prince-54"` and `"dopri54"`	Dormand–Prince embedded 5(4) pair with FSAL property.	[DormandPrince1980]
`"classical-rk4"`	Classical fourth-order Runge–Kutta scheme.	[Kutta1901]
`"cash-karp-54"`	Cash–Karp embedded 5(4) pair with adaptive control weights.	[CashKarp1990]
`"fehlberg-45"`	Runge–Kutta–Fehlberg embedded 5(4) pair.	[Fehlberg1969]

Tableau container

class cubie.integrators.algorithms.generic_erk_tableaus.ERKTableau(a: Tuple[Tuple[float, ...], ...], b: Tuple[float, ...], c: Tuple[float, ...], order: int, b_hat: Tuple[float, ...] | None = None)[source]

Bases: ButcherTableau

Coefficient tableau describing an explicit Runge–Kutta scheme.

References

[Heun1900]

K. Heun. Neue Methoden zur approximativen Integration der Differentialgleichungen einer unabhängigen Veränderlichen. Z. Math. Phys. 45, 1900.

[Ralston1962]

A. Ralston. “Runge-Kutta methods with minimum error bounds.” Math. Comp. 16 (1962).

[BogackiShampine1993]

P. Bogacki and L. F. Shampine. “An efficient Runge-Kutta (4,5) pair.” J. Comput. Appl. Math. 46(1), 1993.

[DormandPrince1980]

J. R. Dormand and P. J. Prince. “A family of embedded Runge-Kutta formulae.” J. Comput. Appl. Math. 6(1), 1980.

[Kutta1901]

W. Kutta. “Beitrag zur näherungsweisen Integration totaler Differentialgleichungen.” Zeitschr. Math. Phys. 46, 1901.

[CashKarp1990]

J. R. Cash and A. H. Karp. “A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides.” ACM Trans. Math. Softw. 16(3), 1990.

[Fehlberg1969]

E. Fehlberg. Low-order classical Runge-Kutta formulas with stepsize control and their application to some heat transfer problems. NASA Technical Report 315, 1969.