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Fixed duplicate ref in docstring
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hgrecco committed Jan 2, 2021
1 parent a6aaf9b commit 33d49c3
Showing 1 changed file with 5 additions and 5 deletions.
10 changes: 5 additions & 5 deletions nbkode/runge_kutta/explicit.py
Original file line number Diff line number Diff line change
Expand Up @@ -154,18 +154,18 @@ class RungeKutta23(FSAL):
class RungeKutta45(FSAL):
"""Explicit Runge-Kutta method of order 5(4).
This uses the Dormand-Prince pair of formulas [1]_. The error is controlled
This uses the Dormand-Prince pair of formulas [2]_. The error is controlled
assuming accuracy of the fourth-order method accuracy, but steps are taken
using the fifth-order accurate formula (local extrapolation is done).
A quartic interpolation polynomial is used for the dense output [2]_.
A quartic interpolation polynomial is used for the dense output [3]_.
Can be applied in the complex domain.
References
----------
.. [1] J. R. Dormand, P. J. Prince, "A family of embedded Runge-Kutta
.. [2] J. R. Dormand, P. J. Prince, "A family of embedded Runge-Kutta
formulae", Journal of Computational and Applied Mathematics, Vol. 6,
No. 1, pp. 19-26, 1980.
.. [2] L. W. Shampine, "Some Practical Runge-Kutta Formulas", Mathematics
.. [3] L. W. Shampine, "Some Practical Runge-Kutta Formulas", Mathematics
of Computation,, Vol. 46, No. 173, pp. 135-150, 1986.
"""

Expand All @@ -182,7 +182,7 @@ class RungeKutta45(FSAL):
B = np.array([35 / 384, 0, 500 / 1113, 125 / 192, -2187 / 6784, 11 / 84])
C = np.array([0, 1 / 5, 3 / 10, 4 / 5, 8 / 9, 1])

# Corresponds to the optimum value of c_6 from [2]_.
# Corresponds to the optimum value of c_6 from [3]_.
P = np.array(
[
[
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