### 1 unstable release

0.1.0 | Sep 11, 2018 |
---|

#**5** in #ode

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**BSD-3-Clause**

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# 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 = "0.1.2"
```

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