Struct Verner8

pub struct Verner8 {
    pub abs_tol: TensorRank0,
    pub rel_tol: TensorRank0,
    pub dt_beta: TensorRank0,
    pub dt_expn: TensorRank0,
    pub dt_init: TensorRank0,
}

Explicit, thirteen-stage, eighth-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)

\cdots

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

---

1. J.H. Verner, Numer. Algor. 53, 383 (2010). ↩

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.

dt_init: TensorRank0

Initial relative time step.

Trait Implementations

impl Debug for Verner8

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

Formats the value using the given formatter.

impl Default for Verner8

fn default() -> Self

Returns the “default value” for a type.

impl<Y, U> Explicit<Y, U> for Verner8

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

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

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

impl<Y, U> InterpolateSolution<Y, U> for Verner8

where Y: Tensor + TensorArray, 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 Fn(&TensorRank0, &Y) -> Y, ) -> U

Solution interpolation.