Struct BogackiShampine 

pub struct BogackiShampine {
    pub abs_tol: Scalar,
    pub rel_tol: Scalar,
    pub dt_beta: Scalar,
    pub dt_expn: Scalar,
    pub dt_cut: Scalar,
    pub dt_min: Scalar,
}

Explicit, three-stage, third-order, variable-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)

k_3 = f(t_n + \tfrac{3}{4} h, y_n + \tfrac{3}{4} h k_2)

y_{n+1} = y_n + \frac{h}{9}\left(2k_1 + 3k_2 + 4k_3\right)

k_4 = f(t_{n+1}, y_{n+1})

e_{n+1} = \frac{h}{72}\left(-5k_1 + 6k_2 + 8k_3 - 9k_4\right)

---

1. P. Bogacki and L.F. Shampine, Appl. Math. Lett. 2, 321 (1989). ↩

Fields

abs_tol: Scalar

Absolute error tolerance.

rel_tol: Scalar

Relative error tolerance.

dt_beta: Scalar

Multiplier for adaptive time steps.

dt_expn: Scalar

Exponent for adaptive time steps.

dt_cut: Scalar

Cut back factor for the time step.

dt_min: Scalar

Minimum value for the time step.

Trait Implementations

impl Debug for BogackiShampine

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

Formats the value using the given formatter.

impl Default for BogackiShampine

fn default() -> Self

Returns the “default value” for a type.

impl<Y, U> Explicit<Y, U> for BogackiShampine

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

const SLOPES: usize = 4

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<Y, Z, U, V> ExplicitDaeVariableStepExplicit<Y, Z, U, V> for BogackiShampine

where Self: ExplicitDaeVariableStepFirstSameAsLast<Y, Z, U, V>, Y: Tensor, Z: Tensor, U: TensorVec<Item = Y>, V: TensorVec<Item = Z>, for<'a> &'a Y: Mul<Scalar, Output = Y> + Sub<&'a Y, Output = Y>,

fn slopes_solve( evolution: impl FnMut(Scalar, &Y, &Z) -> Result<Y, String>, solution: impl FnMut(Scalar, &Y, &Z) -> Result<Z, String>, y: &Y, z: &Z, t: Scalar, dt: Scalar, k: &mut [Y], y_trial: &mut Y, z_trial: &mut Z, ) -> Result<(), String>

fn slopes_solve_and_error( &self, evolution: impl FnMut(Scalar, &Y, &Z) -> Result<Y, String>, solution: impl FnMut(Scalar, &Y, &Z) -> Result<Z, String>, y: &Y, z: &Z, t: Scalar, dt: Scalar, k: &mut [Y], y_trial: &mut Y, z_trial: &mut Z, ) -> Result<Scalar, String>

fn step_solve( &self, _: impl FnMut(Scalar, &Y, &Z) -> Result<Y, String>, y: &mut Y, z: &mut Z, t: &mut Scalar, y_sol: &mut U, z_sol: &mut V, t_sol: &mut Vector, dydt_sol: &mut U, dt: &mut Scalar, k: &mut [Y], y_trial: &Y, z_trial: &Z, e: Scalar, ) -> Result<(), String>

fn integrate_explicit_dae_variable_step( &self, evolution: impl FnMut(Scalar, &Y, &Z) -> Result<Y, String>, solution: impl FnMut(Scalar, &Y, &Z) -> Result<Z, String>, time: &[Scalar], initial_condition: (Y, Z), ) -> Result<(Vector, U, U, V), IntegrationError>

fn interpolate_explicit_dae_variable_step( &self, evolution: impl FnMut(Scalar, &Y, &Z) -> Result<Y, String>, solution: impl FnMut(Scalar, &Y, &Z) -> Result<Z, String>, time: &Vector, tp: &Vector, yp: &U, zp: &V, ) -> Result<(U, U, V), IntegrationError>

impl<Y, Z, U, V> ExplicitDaeVariableStepFirstSameAsLast<Y, Z, U, V> for BogackiShampine

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

fn slopes_solve_and_error_fsal( evolution: impl FnMut(Scalar, &Y, &Z) -> Result<Y, String>, solution: impl FnMut(Scalar, &Y, &Z) -> Result<Z, String>, y: &Y, z: &Z, t: Scalar, dt: Scalar, k: &mut [Y], y_trial: &mut Y, z_trial: &mut Z, ) -> Result<Scalar, String>

fn step_solve_fsal( &self, y: &mut Y, z: &mut Z, t: &mut Scalar, y_sol: &mut U, z_sol: &mut V, t_sol: &mut Vector, dydt_sol: &mut U, dt: &mut Scalar, k: &mut [Y], y_trial: &Y, z_trial: &Z, e: Scalar, ) -> Result<(), String>

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

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

fn abs_tol(&self) -> Scalar

Returns the absolute error tolerance.

fn rel_tol(&self) -> Scalar

Returns the relative error tolerance.

fn dt_beta(&self) -> Scalar

Returns the multiplier for adaptive time steps.

fn dt_expn(&self) -> Scalar

Returns the exponent for adaptive time steps.

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.

impl<Y, U> VariableStepExplicit<Y, U> for BogackiShampine

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

fn error(dt: Scalar, k: &[Y]) -> Result<Scalar, String>

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

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

fn step( &self, _function: impl FnMut(Scalar, &Y) -> Result<Y, String>, y: &mut Y, t: &mut Scalar, y_sol: &mut U, t_sol: &mut Vector, dydt_sol: &mut U, dt: &mut Scalar, k: &mut [Y], y_trial: &Y, e: Scalar, ) -> Result<(), String>

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

fn interpolate_variable_step( time: &Vector, tp: &Vector, yp: &U, function: impl FnMut(Scalar, &Y) -> Result<Y, String>, ) -> Result<(U, U), IntegrationError>

fn time_step(&self, error: Scalar, dt: &mut Scalar)

Provides the adaptive time step as a function of the error.

impl<Y, U> VariableStepExplicitFirstSameAsLast<Y, U> for BogackiShampine

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

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

fn step_fsal( &self, y: &mut Y, t: &mut Scalar, y_sol: &mut U, t_sol: &mut Vector, dydt_sol: &mut U, dt: &mut Scalar, k: &mut [Y], y_trial: &Y, e: Scalar, ) -> Result<(), String>

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

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