verry.integrate.eilo

class verry.integrate.eilo(order=15, rtol=1e-10, atol=1e-10, max_tries=5, min_step=None, max_step=None)

Bases: AdaptiveStepIntegratorFactory, Generic

Factory for creating Integrator based on Eijgenraam and Lohner’s algorithm.

See [1][2][3] for more details on the theory.

Parameters:

• order (int, default=15) – Degree of Taylor polynomial. order must be greater than or equal to 3.

• rtol (default=1e-10) – Relative tolerance.

• atol (default=1e-10) – Absolute tolerance.

• max_tries (int, default=5) – Maximum number of trials to verify the existence conditions of the solution.

• min_step (default=0.0) – Allowed minimum step size. If adaptive stepping produced a step size that is smaller than min_step, step size is set to min_step.

• max_step (default=inf) – Allowed maximum step size. If adaptive stepping produced a step size that is greater than max_step, step size is set to max_step.

References

[1]

P. Eijgenraam, The solution of initial value problems using interval arithmetic: formulation and analysis of an algorithm. Amsterdam, Nederland: CWI, 1981. [Online]. Available: https://ir.cwi.nl/pub/13004/

[2]

R. J. Lohner, “Enclosing the Solutions of Ordinary Initial and Boundary Value Problem,” in Computerarithmetic, E. Kaucher, U. Kulisch, and Ch. Ullrich, Eds. Stuttgart, Germany: B. G. Teubner, 1987, pp. 225–286.

[3]

R. J. Lohner, “Computation of guaranteed enclosures for the solutions of ordinary initial and boundary value problems,” in Computational Ordinary Differential Equations, J. R. Cash and I. Gladwell, Eds. Oxford, UK: Clarendon Press, 1992, pp. 425–435.

copy()

Return a shallow copy of the factory.

create(fun, t0, y0, t_bound)

Create Integrator.

Parameters:

• fun (Callable) – Right-hand side of the system. The calling signature is fun(t, *y).

• t0 (Interval) – Initial time.

• y0 (IntervalMatrix | Sequence[Interval]) – Initial state.

• t_bound (Interval) – Boundary time. Its infimum must be greater than the supremum of t0.

Return type:

Integrator