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RK4Rule38

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RK4Rule38#

class brainpy.integrators.ode.RK4Rule38(f, var_type=None, dt=None, name=None, show_code=False, state_delays=None, neutral_delays=None)[source]#

3/8-rule fourth-order method for ODEs.

A slight variation of “the” Runge–Kutta method is also due to Kutta in 1901 [1] and is called the 3/8-rule. The primary advantage this method has is that almost all of the error coefficients are smaller than in the popular method, but it requires slightly more FLOPs (floating-point operations) per time step.

It has the characteristics of:

  • method stage = 4

  • method order = 4

  • Butcher Tables:

\[\begin{split}\begin{array}{c|cccc} 0 & 0 & 0 & 0 & 0 \\ 1 / 3 & 1 / 3 & 0 & 0 & 0 \\ 2 / 3 & -1 / 3 & 1 & 0 & 0 \\ 1 & 1 & -1 & 1 & 0 \\ \hline & 1 / 8 & 3 / 8 & 3 / 8 & 1 / 8 \end{array}\end{split}\]

References

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