Crate numint

  

ODE solvers and numerical integration in Rust.

Overview

At its core, this crate is designed to work with scalar-valued, vector-valued, and matrix-valued ordinary differential equations.

ODE Type	Function Signature
scalar-valued	$$\frac{dy}{dt}=f(t,y)\quad\quad\left(f:\mathbb{R}\times\mathbb{R}\to\mathbb{R}\right)$$
vector-valued	$$\frac{d\mathbf{y}}{dt}=\mathbf{f}(t,\mathbf{y})\quad\quad\left(\mathbf{f}:\mathbb{R}\times\mathbb{R}^{p}\to\mathbb{R}^{p}\right)$$
matrix-valued	$$\frac{d\mathbf{Y}}{dt}=\mathbf{F}(t,\mathbf{Y})\quad\quad\left(\mathbf{F}:\mathbb{R}\times\mathbb{R}^{p\times r}\to\mathbb{R}^{p\times r}\right)$$

Initial Value Problem (IVP) Solver

The solve_ivp() function is a general purpose IVP solver with the following features:

• it accepts a generic parameter defining the integration method
• it can be used for scalar-valued, vector-valued, and matrix-valued problems (this is accomplished by accepting another generic parameter defining the type of the ODE state)
  • any types of vectors or matrices can be used with this function as long as they implement the OdeState trait (see The OdeState trait section below).

Integration Methods

Runge-Kutta Methods

Integration Method	Order	Implementation
Euler Method	2	Euler
Midpoint Method	2	RK2
Heun’s Second-Order Method	2	RK2Heun
Ralston’s Second-Order Method	2	RK2Ralston
Classic (Kutta’s) Third-Order method	2	RK3
Heun’s Third-Order Method	3	RK3Heun
Ralston’s Third-Order Method	3	RK3Ralston
Strong Stability Preserving Runge-Kutta Third-Order Method	3	SSPRK3
(Classic) Runge-Kutta Fourth-Order Method	4	RK4
Ralston’s Fourth-Order Method	4	RK4Ralston
3/8 Rule Fourth Order Method	4	RK438

The OdeState trait

To allow users to use their favorite vector and matrix representations, this crate defines the OdeState trait. As long as the ODE state trait is implemented for a type, you can use that type to define an ODE to be solved using this crate.

This crate already defines the OdeState for a variety of different types from the standard library, nalgebra, and ndarray. For a full list, refer to the OdeState documentation. This crate also provides macros to automate the implementation of the OdeState trait for types that implement linalg_traits::Scalar, linalg_traits::Vector, or linalg_traits::Matrix traits.

Macro	Description
impl_ode_state_for_scalar!	Implement OdeState for a scalar type already implementing the linalg_traits::Scalar trait.
impl_ode_state_for_dvector!	Implement OdeState for a dynamically-sized vector type already implementing the linalg_traits::Vector trait.
impl_ode_state_for_svector!	Implement OdeState for a statically-sized vector type already implementing the linalg_traits::Vector trait.
impl_ode_state_for_dmatrix!	Implement OdeState for a dynamically-sized matrix type already implementing the linalg_traits::Matrix trait.
impl_ode_state_for_smatrix!	Implement OdeState for a statically-sized matrix type already implementing the linalg_traits::Matrix trait.

Macros

impl_ode_state_for_dmatrix

Macro to implement the OdeState trait for dynamically-sized matrix types.

impl_ode_state_for_dvector

Macro to implement the OdeState trait for dynamically-sized vector types.

impl_ode_state_for_scalar

Macro to implement the OdeState trait for scalar types.

impl_ode_state_for_smatrix

Macro to implement the OdeState trait for statically-sized matrix types.

impl_ode_state_for_svector

Macro to implement the crate::OdeState trait for statically-sized vector types.

Structs

Euler

Euler (first-order) method.

RK2

Midpoint (second-order) method.

RK3

Classic (Kutta’s) third-order method.

RK4

Classic Runge-Kutta fourth-order method.

RK2Heun

Heun’s second-order method.

RK2Ralston

Ralston’s second-order method.

RK3Heun

Heun’s third-order method.

RK3Ralston

Ralston’s third-order method.

RK4Ralston

Ralston’s fourth-order method.

RK438

3/8 rule fourth-order method.

SSPRK3

Strong stability preserving Runge-Kutta third-order method.

Solution

Solution of an ordinary differential equation dy/dt = f(t,y).

Enums

StateIndex

Index for indexing into ODE state.

Traits

IntegrationMethod

Trait defining an integration method.

OdeState

Trait defining an ODE solver state (i.e. the dependent variable in an ODE).

Functions

solve_ivp

Solve an initial value problem.