Crate lazyivy

Expand description

§lazyivy

lazyivy is a Rust crate that provides tools to solve initial value problems of the form dY/dt = F(t, Y) using Runge-Kutta methods.

The algorithms are implemented using the struct RungeKutta that implements Iterator. The following Runge-Kutta methods are implemented currently, and more will be added in the near future.

Euler 1
Ralston 2
Huen-Euler 2(1)
Bogacki-Shampine 3(2)
Fehlberg 4(5)
Dormand-Prince 5(4)

Where p is the order of the method and p* is the order of the error estimator step.

§Lazy integration

RungeKutta implements the Iterator trait. Each .next() call advances the iteration to the next Runge-Kutta step and returns a tuple (t, y), where t is the dependent variable and y is Array1<f64>, which can be used to solve systems of ODEs.

Note that each Runge-Kutta step contains s number of internal stages. Using lazyivy, there is no way at present to access the integration values for these inner stages. The next() call returns the final result for each step, summed over all stages.

The lazy implementation of Runge-Kutta means that you can consume the iterator in different ways. For e.g., you can use .last() to keep only the final result, .collect() to gather the state at all steps, .map() to chain the iterator with another, etc. You may also choose to use it in a for loop and implement you own logic for modifying the step-size or customizing the stop condition.

§Usage:

After adding lazyivy to Cargo.toml, create an initial value problem using the various new_* methods. Here is an example showing how to solve the Brusselator.

use lazyivy::RungeKutta;
use ndarray::{Array, Array1};
  
  
fn brusselator(t: &f64, y: &Array1<f64>) -> Array1<f64> {
    Array::from_vec(vec![
        1. + y[0].powi(2) * y[1] - 4. * y[0],
        3. * y[0] - y[0].powi(2) * y[1],
    ])
}
  
fn main() -> Result<(), String> {
    let t0: f64 = 0.;
    let y0 = Array::from_vec(vec![1.5, 3.]);
    let absolute_tol = Array::from_vec(vec![1.0e-4, 1.0e-4]);
    let relative_tol = Array::from_vec(vec![1.0e-4, 1.0e-4]);
  
    // Instantiate a integrator for an ODE system with adaptive step-size Runge-Kutta.
  
    let mut integrator = RungeKutta::builder(brusselator, |t, _| *t > 40.)
        .initial_condition(t0, y0)
        .initial_step_size(0.025)
        .method("fehlberg", true)
        .tolerances(absolute_tol, relative_tol)
        .set_max_step_size(0.25)
        .build()?;
  
    // For adaptive algorithms, you can use this to improve the initial guess for the step size.
    integrator.set_step_size(&integrator.guess_initial_step());
  
    // Perform the iterations and print each state.
    for item in integrator {
        println!("{:?}", item)   // Prints the tuple (t, array[y1, y2]) at each iteration
    }

    Ok(())
}

Re-exports§

pub use crate::explicit::RungeKutta;

Modules§