Numerical methods to solve ordinary differential equations (ODEs) in Rust.
To start using the crate in your project, add the following dependency in your project's Cargo.toml file:
rust
[dependencies]
ode-solvers = "0.2.0"
Then, in your main file, add
rust
extern crate ode-solvers;
use ode-solvers::*;
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
rust
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:
rust
extern crate nalgebra as na;
type State = VectorN<f64, na::U9>;
The first order ODE(s) must be defined in a function with the following signature
rust
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).
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:
rust
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.
rust
let mut stepper = Dopri5::new(system, x0, x_end, dx, y0, rtol, atol);
The system is integrated using
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let res = stepper.integrate();
and the results are retrieved with
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let x_out = stepper.x_out();
let y_out = stepper.y_out();
See the homepage for more details.
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.