Struct ImplicitMidpoint 

pub struct ImplicitMidpoint { /* private fields */ }

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

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

t_{n+1} = t_n + h

k_1 = f(t_n + \tfrac{1}{2} h, \tfrac{1}{2} y_n + \tfrac{1}{2} y_{n+1})

y_{n+1} = y_n + hk_1

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1. Also known as the implicit midpoint method. ↩

Trait Implementations

impl Debug for Midpoint

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

Formats the value using the given formatter.

impl Default for Midpoint

fn default() -> Midpoint

Returns the “default value” for a type.

impl FixedStep for Midpoint

fn dt(&self) -> Scalar

Returns the time step.

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

where Y: Tensor, for<'a> &'a Y: Mul<Scalar, Output = Y> + Add<&'a Y, 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 Midpoint

where Y: Tensor, for<'a> &'a Y: Mul<Scalar, Output = Y> + Add<&'a Y, 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> OdeSolver<Y, U> for Midpoint

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