Struct DormandPrince

pub struct DormandPrince {
    pub abs_tol: Scalar,
    pub rel_tol: Scalar,
    pub dt_beta: Scalar,
    pub dt_expn: Scalar,
}

Explicit, six-stage, fifth-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}{5} h, y_n + \tfrac{1}{5} h k_1)

k_3 = f(t_n + \tfrac{3}{10} h, y_n + \tfrac{3}{40} h k_1 + \tfrac{9}{40} h k_2)

k_4 = f(t_n + \tfrac{4}{5} h, y_n + \tfrac{44}{45} h k_1 - \tfrac{56}{15} h k_2 + \tfrac{32}{9} h k_3)

k_5 = f(t_n + \tfrac{8}{9} h, y_n + \tfrac{19372}{6561} h k_1 - \tfrac{25360}{2187} h k_2 + \tfrac{64448}{6561} h k_3 - \tfrac{212}{729} h k_4)

k_6 = f(t_n + h, y_n + \tfrac{9017}{3168} h k_1 - \tfrac{355}{33} h k_2 - \tfrac{46732}{5247} h k_3 + \tfrac{49}{176} h k_4 - \tfrac{5103}{18656} h k_5)

y_{n+1} = y_n + h\left(\frac{35}{384}\,k_1 + \frac{500}{1113}\,k_3 + \frac{125}{192}\,k_4 - \frac{2187}{6784}\,k_5 + \frac{11}{84}\,k_6\right)

k_7 = f(t_{n+1}, y_{n+1})

e_{n+1} = \frac{h}{5}\left(\frac{71}{11520}\,k_1 - \frac{71}{3339}\,k_3 + \frac{71}{384}\,k_4 - \frac{17253}{67840}\,k_5 + \frac{22}{105}\,k_6 - \frac{1}{8}\,k_7\right)

h_{n+1} = \beta h \left(\frac{e_\mathrm{tol}}{e_{n+1}}\right)^{1/p}

---

1. J.R. Dormand and P.J. Prince, J. Comput. Appl. Math. 6, 19 (1980). ↩

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.

Trait Implementations

impl Debug for DormandPrince

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

Formats the value using the given formatter.

impl Default for DormandPrince

fn default() -> Self

Returns the “default value” for a type.

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

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

const SLOPES: usize = 7usize

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, U> InterpolateSolution<Y, U> for DormandPrince

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.