Crate differential_equations

differential-equations

A Rust library for solving various types of differential equations.

Overview

This library provides numerical solvers for different classes of differential equations:

• Ordinary Differential Equations (ODE)

  • Initial value problems (ODEProblem)
  • Fixed and adaptive step methods
  • Event detection
  • Customizable output control

• Delay Differential Equations (DDE)

  • Constant delays
  • State-dependent delays
  • Same features as ODEs

• Stochastic Differential Equations (SDE)

  • Drift-diffusion equations
  • User controlled random number generation
  • Same features as ODEs

Feature Flags

• polars: Enable converting Solution to Polars DataFrame using Solution.to_polars()

Example (ODE)

 use differential_equations::prelude::*;
 use nalgebra::{SVector, vector};

 pub struct LinearEquation {
     pub a: f64,
     pub b: f64,
 }

 impl ODE<f64, SVector<f64, 1>> for LinearEquation {
     fn diff(&self, _t: f64, y: &SVector<f64, 1>, dydt: &mut SVector<f64, 1>) {
         dydt[0] = self.a + self.b * y[0];
     }
 }

 fn main() {
     let system = LinearEquation { a: 1.0, b: 2.0 };
     let t0 = 0.0;
     let tf = 1.0;
     let y0 = vector![1.0];
     let problem = ODEProblem::new(system, t0, tf, y0);
     let mut solver = ExplicitRungeKutta::dop853().rtol(1e-8).atol(1e-6);
     let solution = match problem.solve(&mut solver) {
         Ok(sol) => sol,
         Err(e) => panic!("Error: {:?}", e),
     };

     for (t, y) in solution.iter() {
        println!("t: {:.4}, y: {:.4}", t, y[0]);
     }
 }

License

Copyright 2025 Ryan D. Gast

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

    http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.

Re-exports

pub use solout::Solout;

Modules

alias

Type Alias for readablity

dde

Delay Differential Equations (DDE) Module

derive

interpolate

Interpolation Methods for the ODEProblem struct when solving the system.

linalg

Linear algebra helper operations

methods

Numerical Methods for Differential Equations

ode

Ordinary Differential Equations (ODE) Module

prelude

Prelude module for the Differential Equations library.

sde

Stochastic Differential Equations (SDE) Module

solout

Solout trait and common implementations for controlling the output of differential equation solvers.

traits

Defines Generics for the library. Includes generics for the floating point numbers.

utils

Structs

Solution

Solution of returned by differential equation solvers

Enums

ControlFlag

Control flag for solver execution flow

Error

Error for Differential Equations Crate

Status

Status for solving differential equations