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.
You can install extensisq from PyPI:
pip install extensisq
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:
- Lotka Volterra equation, all methods
- Duffing's equation, Bogacki Shampine method
- Non-smooth problem, Cash Karp method
[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