Struct BackwardEuler 

pub struct BackwardEuler { /* private fields */ }

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. ↩

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() -> BackwardEuler

Returns the “default value” for a type.

impl FixedStep for BackwardEuler

fn dt(&self) -> Scalar

Returns the time step.

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

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

fn hessian( &self, jacobian: impl FnMut(Scalar, &Y) -> Result<J, IntegrationError>, _t: Scalar, _y: &Y, t_trial: Scalar, y_trial: &Y, dt: Scalar, ) -> Result<J, String>

fn integrate( &self, function: impl FnMut(Scalar, &Y) -> Result<Y, IntegrationError>, jacobian: impl FnMut(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 Y: Tensor, for<'a> &'a Y: Mul<Scalar, Output = Y> + Sub<&'a Y, Output = Y>, U: TensorVec<Item = Y>,

fn residual( &self, function: impl FnMut(Scalar, &Y) -> Result<Y, IntegrationError>, _t: Scalar, y: &Y, t_trial: Scalar, y_trial: &Y, dt: Scalar, ) -> Result<Y, String>

fn integrate( &self, function: impl FnMut(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> OdeIntegrator<Y, U> for BackwardEuler

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