The Bogacki–Shampine method for ODEs.

The Bogacki–Shampine method was proposed by Przemysław Bogacki and Lawrence F. Shampine in 1989 (Bogacki & Shampine 1989). The Bogacki–Shampine method is a Runge–Kutta method of order three with four stages with the First Same As Last (FSAL) property, so that it uses approximately three function evaluations per step. It has an embedded second-order method which can be used to implement adaptive step size.

It has the characteristics of:

• method stage = 4

• method order = 3

• Butcher Tables:

$\begin{split}\begin{array}{l|lll} 0 & & & \\ 1 / 2 & 1 / 2 & & \\ 3 / 4 & 0 & 3 / 4 & \\ 1 & 2 / 9 & 1 / 3 & 4 / 9 \\ \hline & 2 / 9 & 1 / 3 & 4 / 90 \\ & 7 / 24 & 1 / 4 & 1 / 3 & 1 / 8 \end{array}\end{split}$

References

1

https://en.wikipedia.org/wiki/Bogacki%E2%80%93Shampine_method

2

Bogacki, Przemysław; Shampine, Lawrence F. (1989), “A 3(2) pair of Runge–Kutta formulas”, Applied Mathematics Letters, 2 (4): 321–325, doi:10.1016/0893-9659(89)90079-7

__init__(f, var_type=None, dt=None, name=None, adaptive=None, tol=None, show_code=False, state_delays=None, neutral_delays=None)#

Methods

 __init__(f[, var_type, dt, name, adaptive, ...]) build() load_states(filename[, verbose]) Load the model states. nodes([method, level, include_self]) Collect all children nodes. register_implicit_nodes(*nodes, **named_nodes) register_implicit_vars(*variables, ...) save_states(filename[, variables]) Save the model states. set_integral(f) Set the integral function. train_vars([method, level, include_self]) The shortcut for retrieving all trainable variables. unique_name([name, type_]) Get the unique name for this object. vars([method, level, include_self]) Collect all variables in this node and the children nodes.

Attributes

 A B1 B2 C arguments All arguments when calling the numer integrator of the differential equation. dt The numerical integration precision. integral The integral function. name Name of the model. neutral_delays neutral delays. parameters The parameters defined in the differential equation. state_delays State delays. variables The variables defined in the differential equation.