Struct Midpoint 

pub struct Midpoint { /* private fields */ }

Explicit, two-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, y_n)

k_2 = f(t_n + \tfrac{1}{2} h, y_n + \tfrac{1}{2} h k_1)

y_{n+1} = y_n + h k_2

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1. Also known as the explicit 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<Y, U, V, T> Explicit<Y, U, V, T> for Midpoint

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

const SLOPES: usize = 2

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

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

impl<T> FixedStep<T> for Midpoint

fn dt(&self) -> Quantity<T>

Returns the time step.

impl<Y, U, V, T> FixedStepExplicit<Y, U, V, T> for Midpoint

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

type Tableau = Tableau

Butcher tableau of this method.

fn integrate_fixed_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>

fn step( &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<(), String>

impl<Y, U> OdeIntegrator<Y, U> for Midpoint

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