#ode #math #solver #equations

ode_solvers

Numerical methods to solve ordinary differential equations (ODEs) in Rust

1 unstable release

0.1.0 Sep 11, 2018

#5 in #ode

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ODE-solvers

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Homepage Documentation

Numerical methods to solve ordinary differential equations (ODEs) in Rust.

Installation

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

[dependencies]
ode-solvers = "0.1.2"

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>;

Function definition

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

fn f(x: f64, y: &State, dy: &mut State)

where the first argument is the independent variable (usually time) and the second one is a vector containing the dependent variable(s), and the third one will contain the output of the function (namely the derivative(s) of y with respect to x).

Method selection

The following explicit Runge-Kutta methods are implemented in the current version 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. 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();

and the results are retrieved with

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

See the homepage for more details.

Changelog

  • [0.1.2]
    • Changed the signature of the function defining the ODE(s) to reduce the number of allocations.
  • [0.1.1]
    • Added automatic stiffness detection
    • x_end - x0 can be positive or negative
    • Fixed bug in sparse output of dopri5
    • Added Lorenz attractor example

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

~2MB
~43K SLoC