Struct BackwardEuler 

pub struct BackwardEuler {
    pub dt_cut: Scalar,
    pub dt_min: Scalar,
}

Implicit, single-stage, first-order, fixed-step, Runge-Kutta method.¹

\frac{dy}{dt} = f(t, y)

t_{n+1} = t_n + h

k_1 = f(t_{n+1}, y_{n+1})

y_{n+1} = y_n + hk_1

---

1. Also known as the backward Euler method. ↩

Fields

dt_cut: Scalar

Cut back factor for the time step.

dt_min: Scalar

Minimum value for the time step.

Trait Implementations

impl Debug for BackwardEuler

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

Formats the value using the given formatter.

impl Default for BackwardEuler

fn default() -> Self

Returns the “default value” for a type.

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

where Self: InterpolateSolution<Y, U>, Y: Jacobian + Solution + Div<J, Output = Y>, for<'a> &'a Y: Mul<Scalar, Output = Y> + Sub<&'a Y, Output = Y>, J: Hessian + TensorArray, U: TensorVec<Item = Y>, Vector: From<Y>,

fn integrate( &self, function: impl Fn(Scalar, &Y) -> Result<Y, IntegrationError>, jacobian: impl Fn(Scalar, &Y) -> Result<J, IntegrationError>, time: &[Scalar], initial_condition: Y, solver: impl FirstOrderRootFinding<Y, J, Y>, ) -> Result<(Vector, U, U), IntegrationError>

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

impl<Y, U> ImplicitZerothOrder<Y, U> for BackwardEuler

where Self: InterpolateSolution<Y, U>, Y: Solution, for<'a> &'a Y: Mul<Scalar, Output = Y> + Sub<&'a Y, Output = Y>, U: TensorVec<Item = Y>, Vector: From<Y>,

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

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

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

where Y: Jacobian + Solution + TensorArray, for<'a> &'a Y: Mul<Scalar, Output = Y> + Sub<&'a Y, Output = Y>, U: TensorVec<Item = Y>, Vector: From<Y>,

fn interpolate( &self, _time: &Vector, _tp: &Vector, _yp: &U, _function: impl FnMut(Scalar, &Y) -> Result<Y, String>, ) -> Result<(U, U), IntegrationError>

Solution interpolation.

impl<Y, U> OdeSolver<Y, U> for BackwardEuler

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

fn abs_tol(&self) -> Scalar

Returns the absolute error tolerance.

fn dt_cut(&self) -> Scalar

Returns the cut back factor for function errors.

fn dt_min(&self) -> Scalar

Returns the minimum value for the time step.