Struct BogackiShampine

pub struct BogackiShampine {
    pub abs_tol: TensorRank0,
    pub rel_tol: TensorRank0,
    pub dt_beta: TensorRank0,
    pub dt_expn: TensorRank0,
}

Explicit, three-stage, third-order, variable-step, Runge-Kutta method.¹

\frac{dy}{dt} = f(t, y)

t_{n+1} = t_n + h

k_1 = f(t_n, y_n)

k_2 = f(t_n + \tfrac{1}{2} h, y_n + \tfrac{1}{2} h k_1)

k_3 = f(t_n + \tfrac{3}{4} h, y_n + \tfrac{3}{4} h k_2)

y_{n+1} = y_n + \frac{h}{9}\left(2k_1 + 3k_2 + 4k_3\right)

k_4 = f(t_{n+1}, y_{n+1})

e_{n+1} = \frac{h}{72}\left(-5k_1 + 6k_2 + 8k_3 - 9k_4\right)

h_{n+1} = \beta h \left(\frac{e_\mathrm{tol}}{e_{n+1}}\right)^{1/p}

---

1. P. Bogacki and L.F. Shampine, Appl. Math. Lett. 2, 321 (1989). ↩

Fields

abs_tol: TensorRank0

Absolute error tolerance.

rel_tol: TensorRank0

Relative error tolerance.

dt_beta: TensorRank0

Multiplier for adaptive time steps.

dt_expn: TensorRank0

Exponent for adaptive time steps.

Trait Implementations

impl Debug for BogackiShampine

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Default for BogackiShampine

fn default() -> Self

Returns the “default value” for a type.

impl<Y, U> Explicit<Y, U> for BogackiShampine

where Self: InterpolateSolution<Y, U>, Y: Tensor, for<'a> &'a Y: Mul<TensorRank0, Output = Y> + Sub<&'a Y, Output = Y>, U: TensorVec<Item = Y>,

fn integrate( &self, function: impl FnMut(TensorRank0, &Y) -> Result<Y, IntegrationError>, time: &[TensorRank0], initial_condition: Y, ) -> Result<(Vector, U, U), IntegrationError>

Solves an initial value problem by explicitly integrating a system of ordinary differential equations.

impl<Y, U> InterpolateSolution<Y, U> for BogackiShampine

where Y: Tensor, for<'a> &'a Y: Mul<TensorRank0, Output = Y> + Sub<&'a Y, Output = Y>, U: TensorVec<Item = Y>,

fn interpolate( &self, time: &Vector, tp: &Vector, yp: &U, function: impl FnMut(TensorRank0, &Y) -> Result<Y, IntegrationError>, ) -> Result<(U, U), IntegrationError>

Solution interpolation.