1 unstable release
|0.1.0||Sep 11, 2018|
#5 in #ode
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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.
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::*;
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>;
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).
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|
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:
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();
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.