#ode #math #solver #equations

ode_solvers

ode-solvers is a toolbox to solve first order ordinary differential equations

1 unstable release

0.1.0 Sep 11, 2018

#5 in #ode

Download history 11/week @ 2018-09-12

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ODE-solvers

Ode-solvers is a toolbox offering several methods to solve ordinary differential equations (ODEs) in Rust. The following instructions should get you up and running in no time. For more details, see the homepage.

Importing the crate

To start using the crate in your project, add the following dependency in your project's Cargo.toml file:

[dependencies]
ode-solvers = "0.1.0"

Then, in your main file, add

extern crate ode-solvers;
use ode-solvers::*;

Type alias definition

The numerical integration methods implemented in the crate support multi-dimensional systems. In order to define the dimension of the system, declare a type alias for the state vector. For instance

type State = Vector3<f64>;

The state representation of the system is based on the VectorN<T,D> structure defined in the nalgebra crate. For convenience, ode-solvers re-exports six types to work with systems of dimension 1 to 6: Vector1<T>,..., Vector6<T>. For higher dimensions, the user should import the nalgebra crate and define a VectorN<T,D> where the second type parameter of VectorN is a dimension name defined in nalgebra. Note that the type T must be f64. For instance, for a 9-dimensional system, one would have:

extern crate nalgebra as na;
type State = VectorN<f64, na::U9>;

System definition

The first order ODE(s) must be defined in a function with the following signature

fn system(x: f64, y: &State) -> State

where the first argument is the independent variable (usually time) and the second one is a vector containing the dependent variable(s).

Method selection

The following explicit Runge-Kutta methods are implemented in the current version (0.1.0) of the crate:

Method Name Order Error estimate order Dense output order
Dormand-Prince Dopri5 5 4 4
Dormand-Prince Dop853 8 (5,3) 7

These methods are defined in the modules dopri5 and dop853 and feature:

  • Adaptive step size control
  • Automatic initial step size selection
  • Sparse or dense output

The first step is to bring the desired module into scope:

use ode_solvers::dopri5::*;

Then, a structure is created using the new or the from_param method of the corresponding struct. Refer to the API documentation for a description of the input arguments.

let mut stepper = Dopri5::new(system, x0, x_end, dx, y0, rtol, atol);

The system is integrated using

let res = stepper.integrate();

which returns Result<Stats, IntegrationError>. Upon successful completion, res = Ok(Stats) where Stats is a structure containing some information on the integration process. If an error occurs, res = Err(IntegrationError). Finally, the results can be retrieved with

let x_out = stepper.x_out();
let y_out = stepper.y_out();

Acknowledgments

The algorithms implemented in this crate were originally implemented in FORTRAN by E. Hairer and G. Wanner, Université de Genève, Switzerland. This Rust implementation has been adapted from the C version written by J. Colinge, Université de Genève, Switzerland and the C++ version written by Blake Ashby, Stanford University, USA.

Dependencies

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~42K SLoC