Struct bacon_sci::ivp::RK45

pub struct RK45<N: ComplexField> { /* fields omitted */ }

Runge-Kutta-Fehlberg method for solving an IVP.

Defines the Butch Tableaux for a 5(4) order adaptive runge-kutta method. Uses RKInfo to do the actual solving. Provides an interface for setting the conditions on RKInfo.

Examples

use nalgebra::DVector;
use bacon_sci::ivp::{IVPSolver, RK45, RungeKuttaSolver};
fn derivatives(_t: f64, state: &[f64], _p: &mut ()) -> Result<DVector<f64>, String> {
    Ok(DVector::from_column_slice(state))
}

fn example() -> Result<(), String> {
    let rk45 = RK45::new()
        .with_dt_max(0.1)?
        .with_dt_min(0.001)?
        .with_start(0.0)?
        .with_end(10.0)?
        .with_tolerance(0.0001)?
        .with_initial_conditions(&[1.0])?
        .build();
    let path = rk45.solve_ivp(derivatives, &mut ())?;
    for (time, state) in &path {
        assert!((time.exp() - state.column(0)[0]).abs() < 0.001);
    }
    Ok(())
}

Implementations

impl<N: ComplexField> RK45<N>

pub fn new() -> Self

Trait Implementations

impl<N: Clone + ComplexField> Clone for RK45<N>

pub fn clone(&self) -> RK45<N>

Returns a copy of the value.

pub fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<N: Debug + ComplexField> Debug for RK45<N>

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

Formats the value using the given formatter.

impl<N: ComplexField> Default for RK45<N>

pub fn default() -> Self

Returns the "default value" for a type.

impl<N: ComplexField> From<RK45<N>> for RKInfo<N>

pub fn from(rk: RK45<N>) -> RKInfo<N>

Performs the conversion.

impl<N: ComplexField> RungeKuttaSolver<N> for RK45<N>

pub fn t_coefficients() -> Vec<N::RealField>

Returns a vec of coeffecients to multiply the time step by when getting intermediate results. Upper-left portion of Butch Tableaux

pub fn k_coefficients() -> Vec<Vec<N::RealField>>

Returns the coefficients to use on the k_i's when finding another k_i. Upper-right portion of the Butch Tableax. Should be an NxN-1 matrix, where N is the order of the Runge-Kutta Method (Or order+1 for adaptive methods)

pub fn avg_coefficients() -> Vec<N::RealField>

Coefficients to use when calculating the final step to take. These are the weights of the weighted average of k_i's. Bottom portion of the Butch Tableaux. For adaptive methods, this is the first row of the bottom portion.

pub fn error_coefficients() -> Vec<N::RealField>

Coefficients to use on the k_i's to find the error between the two orders of Runge-Kutta methods. In the Butch Tableaux, this is the first row of the bottom portion minus the second row.

pub fn solve_ivp<T: Clone, F: Fn(N::RealField, &[N], &mut T) -> Result<DVector<N>, String>>(
    self,
    f: F,
    params: &mut T
) -> Result<Vec<(N::RealField, DVector<N>)>, String>

Ideally, call RKInfo.solve_ivp

pub fn with_tolerance(self, tol: N::RealField) -> Result<Self, String>

Set the error tolerance for this solver.

pub fn with_dt_max(self, max: N::RealField) -> Result<Self, String>

Set the maximum time step for this solver.

pub fn with_dt_min(self, min: N::RealField) -> Result<Self, String>

Set the minimum time step for this solver.

pub fn with_start(self, t_initial: N::RealField) -> Result<Self, String>

Set the initial time for this solver.

pub fn with_end(self, t_final: N::RealField) -> Result<Self, String>

Set the end time for this solver.

pub fn with_initial_conditions(self, start: &[N]) -> Result<Self, String>

Set the initial conditions for this solver.

pub fn build(self) -> Self

Build this solver.