Struct bacon_sci::ivp::RK45

pub struct RK45<N, const S: usize>where
    N: ComplexField + FromPrimitive,
    <N as ComplexField>::RealField: FromPrimitive,{ /* private fields */ }

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::SVector;
use bacon_sci::ivp::{RK45, RungeKuttaSolver};
fn derivatives(_t: f64, state: &[f64], _p: &mut ()) -> Result<SVector<f64, 1>, String> {
    Ok(SVector::<f64, 1>::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, const S: usize> RK45<N, S>where N: ComplexField + FromPrimitive + Copy, <N as ComplexField>::RealField: FromPrimitive + Copy,

pub fn new() -> Self

Trait Implementations

impl<N, const S: usize> Clone for RK45<N, S>where N: ComplexField + FromPrimitive + Clone, <N as ComplexField>::RealField: FromPrimitive,

fn clone(&self) -> RK45<N, S>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<N, const S: usize> Debug for RK45<N, S>where N: ComplexField + FromPrimitive + Debug, <N as ComplexField>::RealField: FromPrimitive,

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

Formats the value using the given formatter.

impl<N, const S: usize> From<RK45<N, S>> for RKInfo<N, S, 6>where N: ComplexField + FromPrimitive, <N as ComplexField>::RealField: FromPrimitive,

fn from(rk: RK45<N, S>) -> RKInfo<N, S, 6>

Converts to this type from the input type.

impl<N, const S: usize> RungeKuttaSolver<N, S, 6> for RK45<N, S>where N: ComplexField + FromPrimitive + Copy, <N as ComplexField>::RealField: FromPrimitive + Copy,

fn t_coefficients() -> SVector<N::RealField, 6>

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

fn k_coefficients() -> SMatrix<N::RealField, 6, 6>

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)

fn avg_coefficients() -> SVector<N::RealField, 6>

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.

fn error_coefficients() -> SVector<N::RealField, 6>

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.

fn solve_ivp<T, F>( self, f: F, params: &mut T ) -> Result<Vec<(N::RealField, SVector<N, S>)>, String>where T: Clone, F: FnMut(N::RealField, &[N], &mut T) -> Result<SVector<N, S>, String>,

Ideally, call RKInfo.solve_ivp

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

Set the error tolerance for this solver.

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

Set the maximum time step for this solver.

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

Set the minimum time step for this solver.

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

Set the initial time for this solver.

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

Set the end time for this solver.

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

Set the initial conditions for this solver.

fn build(self) -> Self

Build this solver.