Trait VariableStepExplicit 

pub trait VariableStepExplicit<Y, U, V, T = Time>
where
    Self: Explicit<Y, U, V, T> + VariableStep<T>,
    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: EmbeddedTableau;

    // Provided methods
    fn integrate_variable_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>
       where Self: InterpolateSolution<Y, U, V, T> { ... }
    fn interpolate_variable_step(
        time: &Times<T>,
        tp: &Times<T>,
        yp: &U,
        function: impl FnMut(Quantity<T>, &Y) -> Result<Derivative<Y, T>, String>,
    ) -> Result<(U, V), IntegrationError> { ... }
    fn slopes(
        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> { ... }
    fn error(
        &self,
        dt: Quantity<T>,
        k: &[Derivative<Y, T>],
    ) -> Result<Scalar, String> { ... }
    fn slopes_and_error(
        &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<Scalar, String> { ... }
    fn step(
        &self,
        function: impl FnMut(Quantity<T>, &Y) -> Result<Derivative<Y, T>, String>,
        y: &mut Y,
        t: &mut Quantity<T>,
        y_sol: &mut U,
        t_sol: &mut Times<T>,
        dydt_sol: &mut V,
        k_sol: &mut Vec<V>,
        dt: &mut Quantity<T>,
        k: &mut [Derivative<Y, T>],
        y_trial: &Y,
        e: Scalar,
    ) -> Result<(), String> { ... }
    fn time_step(&self, error: Scalar, tolerance: Scalar, dt: &mut Quantity<T>) { ... }
}

Variable-step explicit integrators for ordinary differential equations.

Required Associated Types

type Tableau: EmbeddedTableau

Butcher tableau of this method’s embedded pair.

Provided Methods

fn integrate_variable_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>

where Self: InterpolateSolution<Y, U, V, T>,

fn interpolate_variable_step( time: &Times<T>, tp: &Times<T>, yp: &U, function: impl FnMut(Quantity<T>, &Y) -> Result<Derivative<Y, T>, String>, ) -> Result<(U, V), IntegrationError>

fn slopes( 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>

Runge–Kutta stages and the propagating solution.

\mathbf{k}_i = \mathbf{f}\!\left(t + c_i h,\ \mathbf{y} + h \sum_{j<i} a_{ij}\, \mathbf{k}_j\right)
,\qquad
\mathbf{y}_{n+1} = \mathbf{y} + h \textstyle\sum_i b_i\,\mathbf{k}_i

fn error( &self, dt: Quantity<T>, k: &[Derivative<Y, T>], ) -> Result<Scalar, String>

Embedded local-error estimate reduced through the error norm.

e_{n+1} = \Big\Vert h \textstyle\sum_i d_i\,\mathbf{k}_i \Big\Vert

fn slopes_and_error( &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<Scalar, String>

fn step( &self, function: impl FnMut(Quantity<T>, &Y) -> Result<Derivative<Y, T>, String>, y: &mut Y, t: &mut Quantity<T>, y_sol: &mut U, t_sol: &mut Times<T>, dydt_sol: &mut V, k_sol: &mut Vec<V>, dt: &mut Quantity<T>, k: &mut [Derivative<Y, T>], y_trial: &Y, e: Scalar, ) -> Result<(), String>

fn time_step(&self, error: Scalar, tolerance: Scalar, dt: &mut Quantity<T>)

Provides the adaptive time step as a function of the error.

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

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety".

Implementors

impl<Y, U, V, T> VariableStepExplicit<Y, U, V, T> for BogackiShampine

where Self: Explicit<Y, U, V, T>, Y: Differentiable<T> + Div<Quantity<T>, Output = Derivative<Y, 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

impl<Y, U, V, T> VariableStepExplicit<Y, U, V, T> for DormandPrince

where Self: Explicit<Y, U, V, T>, 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

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

where Self: Explicit<Y, U, V, T>, 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

impl<Y, U, V, T> VariableStepExplicit<Y, U, V, T> for Verner9

where Self: Explicit<Y, U, V, T>, 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