Struct Verner8

pub struct Verner8 {
    pub abs_tol: Scalar,
    pub rel_tol: Scalar,
    pub dt_beta: Scalar,
    pub dt_expn: Scalar,
}

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: Scalar

Absolute error tolerance.

rel_tol: Scalar

Relative error tolerance.

dt_beta: Scalar

Multiplier for adaptive time steps.

dt_expn: Scalar

Exponent for adaptive time steps.

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

const SLOPES: usize = 13usize

fn integrate( &self, function: impl FnMut(Scalar, &Y) -> Result<Y, String>, time: &[Scalar], 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 Verner8

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

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

Solution interpolation.