extensisq 0.0.1

extend solve_ivp of scipy.integrate with OdeSolver objects

extensisq

This package extends scipy.integrate with OdeSolver objects for the solve_ivp function.

Currently, three explicit Runge Kutta methods of order 5 are implemented:

• Bogacki Shampine: efficient solver with an accurate high order interpolant (and a free low order one) [1]
• Cash Karp: variable order solver tailored to solve non-smooth problems efficiently [2]
• Tsitouras: relatively new solver (2011), optimized with fewer simplifying assumptions [3]

The first two methods have two variants each.

Installation

You can install extensisq from PyPI:

pip install extensisq

Example

Borrowed from the the scipy documentation:

from scipy.integrate import solve_ivp
from extensisq import BS45_i

def exponential_decay(t, y): return -0.5 * y
sol = solve_ivp(exponential_decay, [0, 10], [2, 4, 8], method=BS45_i)

print(sol.t)
print(sol.y)

Note that the object BS45_i is passed, not the string "BS45_i". The other methods (BS45, CK45, CK45_o and Ts45) can be used in a similar way.

More examples are available as notebooks:

1. Lotka Volterra equation, all methods
2. Duffing's equation, Bogacki Shampine method
3. Non-smooth problem, Cash Karp method

References

[1]: P. Bogacki, L.F. Shampine, "An efficient Runge-Kutta (4,5) pair", Computers & Mathematics with Applications, Vol. 32, No. 6, 1996, pp. 15-28, ISSN 0898-1221. https://doi.org/10.1016/0898-1221(96)00141-1

[2]: J. R. Cash, A. H. Karp, "A Variable Order Runge-Kutta Method for Initial Value Problems with Rapidly Varying Right-Hand Sides", ACM Trans. Math. Softw., Vol. 16, No. 3, 1990, pp. 201-222, ISSN 0098-3500. https://doi.org/10.1145/79505.79507

[3]: Ch. Tsitouras, "Runge-Kutta pairs of order 5(4) satisfying only the first column simplifying assumption", Computers & Mathematics with Applications, Vol. 62, No. 2, pp. 770 - 775, 2011. https://doi.org/10.1016/j.camwa.2011.06.002