ode_solvers

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

4 releases

 new 0.2.0 Feb 20, 2019 Oct 20, 2018 Sep 25, 2018 Sep 11, 2018

#3 in #ode

BSD-3-Clause

64KB
1.5K SLoC

ODE-solvers

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 = "0.2.0"
``````

``````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), 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

• [0.2.0]
• Updated dependencies, use slightly more idiomatic Rust.
• [0.1.2]
• Changed the signature of the function defining the ODE(s) to reduce the number of allocations.
• [0.1.1]