Struct Verner8FixedStep 

pub struct Verner8FixedStep { /* private fields */ }

Explicit, twelve-stage, eighth-order, fixed-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

---

1. Fixed-step variant of the Verner 8 method. ↩

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() -> Verner8

Returns the “default value” for a type.

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

where Y: Differentiable<T> + Tensor, Derivative<Y, T>: Mul<Quantity<T>, Output = Y>, for<'a> &'a Y: Mul<Scalar, Output = Y> + Sub<&'a Y, Output = Y>, for<'a> &'a Derivative<Y, T>: Mul<Scalar, Output = Derivative<Y, T>> + Mul<Quantity<T>, Output = Y>, U: TensorVec<Item = Y>, V: TensorVec<Item = Derivative<Y, T>>,

const SLOPES: usize = 12

fn integrate( &self, function: impl FnMut(Quantity<T>, &Y) -> Result<Derivative<Y, T>, String>, time: &[Quantity<T>], initial_condition: Y, ) -> Result<(Times<T>, U, V), IntegrationError>

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

fn integrate_bounded( &self, function: impl FnMut(Quantity<T>, &Y) -> Result<Derivative<Y, T>, String>, bound: impl FnMut(Quantity<T>, &Y) -> Result<Spectrum<T>, String>, safety: Scalar, time: &[Quantity<T>], initial_condition: Y, ) -> Result<(Times<T>, U, V), IntegrationError>

Solves an initial value problem like integrate, subject to a stability bound.

impl<T> FixedStep<T> for Verner8

fn dt(&self) -> Quantity<T>

Returns the time step.

impl<Y, U, V, T> FixedStepExplicit<Y, U, V, T> for Verner8

where Y: Differentiable<T> + Tensor, Derivative<Y, T>: Mul<Quantity<T>, Output = Y>, for<'a> &'a Y: Mul<Scalar, Output = Y> + Sub<&'a Y, Output = Y>, for<'a> &'a Derivative<Y, T>: Mul<Scalar, Output = Derivative<Y, T>> + Mul<Quantity<T>, Output = Y>, U: TensorVec<Item = Y>, V: TensorVec<Item = Derivative<Y, T>>,

type Tableau = Tableau

Butcher tableau of this method.

fn integrate_fixed_step( &self, function: impl FnMut(Quantity<T>, &Y) -> Result<Derivative<Y, T>, String>, time: &[Quantity<T>], initial_condition: Y, ) -> Result<(Times<T>, U, V), IntegrationError>

fn integrate_fixed_step_bounded( &self, function: impl FnMut(Quantity<T>, &Y) -> Result<Derivative<Y, T>, String>, bound: impl FnMut(Quantity<T>, &Y) -> Result<Spectrum<T>, String>, safety: Scalar, time: &[Quantity<T>], initial_condition: Y, ) -> Result<(Times<T>, U, V), IntegrationError>

fn integrate_fixed_step_checked( &self, function: impl FnMut(Quantity<T>, &Y) -> Result<Derivative<Y, T>, String>, check: impl FnMut(Quantity<T>, &Y, Quantity<T>) -> Result<(), IntegrationError>, time: &[Quantity<T>], initial_condition: Y, ) -> Result<(Times<T>, U, V), IntegrationError>

fn step( &self, function: impl FnMut(Quantity<T>, &Y) -> Result<Derivative<Y, T>, String>, y: &Y, t: Quantity<T>, dt: Quantity<T>, k: &mut [Derivative<Y, T>], y_trial: &mut Y, ) -> Result<(), String>

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

where Y: Tensor, U: TensorVec<Item = Y>,

impl<T> Stacked<T> for Verner8FixedStep

fn integrate_stacked<X, UX, UV, UA>( &self, function: impl FnMut(Quantity<T>, &X, &Derivative<X, T>) -> Result<Derivative<Derivative<X, T>, T>, String>, time: &[Quantity<T>], initial_position: X, initial_velocity: Derivative<X, T>, ) -> Result<(Times<T>, UX, UV, UA), IntegrationError>

where Self: Explicit<TensorTuple<X, Derivative<X, T>>, TensorVector<TensorTuple<X, Derivative<X, T>>>, TensorVector<Derivative<TensorTuple<X, Derivative<X, T>>, T>>, T>, X: Differentiable<T> + Tensor, Derivative<X, T>: Differentiable<T> + Tensor, UX: TensorVec<Item = X>, UV: TensorVec<Item = Derivative<X, T>>, UA: TensorVec<Item = Derivative<Derivative<X, T>, T>>,

Solves an initial value problem for dynamics, given the acceleration as a function of time, position, and velocity.

fn integrate_stacked_bounded<X, UX, UV, UA>( &self, function: impl FnMut(Quantity<T>, &X, &Derivative<X, T>) -> Result<Derivative<Derivative<X, T>, T>, String>, bound: impl FnMut(Quantity<T>, &X, &Derivative<X, T>) -> Result<Quantity<T>, String>, safety: Scalar, time: &[Quantity<T>], initial_position: X, initial_velocity: Derivative<X, T>, ) -> Result<(Times<T>, UX, UV, UA), IntegrationError>

where Self: Explicit<TensorTuple<X, Derivative<X, T>>, TensorVector<TensorTuple<X, Derivative<X, T>>>, TensorVector<Derivative<TensorTuple<X, Derivative<X, T>>, T>>, T>, X: Differentiable<T> + Tensor, Derivative<X, T>: Differentiable<T> + Tensor, UX: TensorVec<Item = X>, UV: TensorVec<Item = Derivative<X, T>>, UA: TensorVec<Item = Derivative<Derivative<X, T>, T>>,

Solves an initial value problem like integrate_stacked, subject to a stability bound.

fn integrate_stacked_coupled<X, Y, UX, UV, UA, UY, UR>( &self, function: impl FnMut(Quantity<T>, &X, &Derivative<X, T>, &Y) -> Result<(Derivative<Derivative<X, T>, T>, Derivative<Y, T>), String>, time: &[Quantity<T>], initial_position: X, initial_velocity: Derivative<X, T>, initial_state: Y, ) -> Result<(Times<T>, UX, UV, UA, UY, UR), IntegrationError>

where Self: Explicit<TensorTuple<TensorTuple<X, Derivative<X, T>>, Y>, TensorVector<TensorTuple<TensorTuple<X, Derivative<X, T>>, Y>>, TensorVector<Derivative<TensorTuple<TensorTuple<X, Derivative<X, T>>, Y>, T>>, T>, X: Differentiable<T> + Tensor, Derivative<X, T>: Differentiable<T> + Tensor, Y: Differentiable<T> + Tensor, UX: TensorVec<Item = X>, UV: TensorVec<Item = Derivative<X, T>>, UA: TensorVec<Item = Derivative<Derivative<X, T>, T>>, UY: TensorVec<Item = Y>, UR: TensorVec<Item = Derivative<Y, T>>,

fn integrate_stacked_coupled_bounded<X, Y, UX, UV, UA, UY, UR>( &self, function: impl FnMut(Quantity<T>, &X, &Derivative<X, T>, &Y) -> Result<(Derivative<Derivative<X, T>, T>, Derivative<Y, T>), String>, bound: impl FnMut(Quantity<T>, &X, &Derivative<X, T>, &Y) -> Result<Spectrum<T>, String>, safety: Scalar, time: &[Quantity<T>], initial_position: X, initial_velocity: Derivative<X, T>, initial_state: Y, ) -> Result<(Times<T>, UX, UV, UA, UY, UR), IntegrationError>

where Self: Explicit<TensorTuple<TensorTuple<X, Derivative<X, T>>, Y>, TensorVector<TensorTuple<TensorTuple<X, Derivative<X, T>>, Y>>, TensorVector<Derivative<TensorTuple<TensorTuple<X, Derivative<X, T>>, Y>, T>>, T>, X: Differentiable<T> + Tensor, Derivative<X, T>: Differentiable<T> + Tensor, Y: Differentiable<T> + Tensor, UX: TensorVec<Item = X>, UV: TensorVec<Item = Derivative<X, T>>, UA: TensorVec<Item = Derivative<Derivative<X, T>, T>>, UY: TensorVec<Item = Y>, UR: TensorVec<Item = Derivative<Y, T>>,