Trait ImplicitFirstOrder 

pub trait ImplicitFirstOrder<Y, J, U, V, T = Time>
where
    Self: ImplicitZerothOrder<Y, U, V, T>,
    Y: Differentiate<T> + Tensor,
    J: Differentiate<T> + Tensor,
    U: TensorVec<Item = Y>,
    V: TensorVec<Item = Derivative<Y, T>>,
{
    // Required method
    fn hessian(
        &self,
        jacobian: impl FnMut(Quantity<T>, &Y) -> Result<Derivative<J, T>, IntegrationError>,
        t: Quantity<T>,
        y: &Y,
        t_trial: Quantity<T>,
        y_trial: &Y,
        dt: Quantity<T>,
    ) -> Result<J, String>;

    // Provided method
    fn integrate(
        &self,
        function: impl FnMut(Quantity<T>, &Y) -> Result<Derivative<Y, T>, IntegrationError>,
        jacobian: impl FnMut(Quantity<T>, &Y) -> Result<Derivative<J, T>, IntegrationError>,
        time: &[Quantity<T>],
        initial_condition: Y,
        solver: impl FirstOrderRootFinding<Y, J, Y>,
    ) -> Result<(Times<T>, U, V), IntegrationError> { ... }
}

Implicit integrators for ordinary differential equations using first-order root-finding.

Required Methods

fn hessian( &self, jacobian: impl FnMut(Quantity<T>, &Y) -> Result<Derivative<J, T>, IntegrationError>, t: Quantity<T>, y: &Y, t_trial: Quantity<T>, y_trial: &Y, dt: Quantity<T>, ) -> Result<J, String>

Provided Methods

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

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

\frac{dy}{dt} = f(t, y),\quad y(t_0) = y_0,\quad \frac{\partial f}{\partial y} = J(t, y)

Dyn Compatibility

This trait is not dyn compatible.

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

Implementors

impl<Y, J, U, V, T> ImplicitFirstOrder<Y, J, U, V, T> for BackwardEuler

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

impl<Y, J, U, V, T> ImplicitFirstOrder<Y, J, U, V, T> for Midpoint

where Y: Differentiate<T> + Tensor, Derivative<Y, T>: Mul<Quantity<T>, Output = Y>, J: Differentiate<T> + Tensor + TensorArray, Derivative<J, T>: Mul<Quantity<T>, Output = J>, for<'a> &'a Y: Add<&'a Y, Output = Y> + Sub<&'a Y, Output = Y>, U: TensorVec<Item = Y>, V: TensorVec<Item = Derivative<Y, T>>,

impl<Y, J, U, V, T> ImplicitFirstOrder<Y, J, U, V, T> for Trapezoidal

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