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> Explicit<Y, U> for Midpoint

where Self: OdeSolver<Y, U>, Y: Tensor, for<'a> &'a Y: Mul<Scalar, Output = Y>, U: TensorVec<Item = Y>,

const SLOPES: usize = 2

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

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

impl FixedStep for Midpoint

fn dt(&self) -> Scalar

Returns the time step.

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

where Self: OdeSolver<Y, U>, Y: Tensor, for<'a> &'a Y: Mul<Scalar, Output = Y>, U: TensorVec<Item = Y>,

fn step( &self, function: impl FnMut(Scalar, &Y) -> Result<Y, String>, y: &Y, t: Scalar, dt: Scalar, k: &mut [Y], y_trial: &mut Y, ) -> Result<(), String>

fn integrate_fixed_step( &self, function: impl FnMut(Scalar, &Y) -> Result<Y, String>, time: &[Scalar], initial_condition: Y, ) -> Result<(Vector, U, U), IntegrationError>

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

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