Crate differential_equations

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§differential-equations

A Rust library for solving various types of differential equations.

GitHub Documentation

§Overview

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

§Feature Flags

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

§Example (ODE)

 use differential_equations::ode::*;
 use nalgebra::{SVector, vector};
 
 pub struct LinearEquation {
     pub a: f64,
     pub b: f64,
 }
 
 impl ODE<f64, 1, 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 ivp = IVP::new(system, t0, tf, y0);
     let mut solver = DOP853::new().rtol(1e-8).atol(1e-6);
     let solution = match ivp.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.

Modules§

interpolate
Interpolation Methods for the IVP struct when solving the system.
ode
Ordinary Differential Equations (ODE) Module
traits
Defines Generics for the library. Includes generics for the floating point numbers and state vectors.

Macros§

adaptive_dense_runge_kutta_method
Macro to create a Runge-Kutta solver with dense output capabilities
adaptive_runge_kutta_method
Macro to create an adaptive Runge-Kutta solver with embedded error estimation and interpolation vs cubic Hermite interpolation.
matrix
Construct a fixed-size matrix directly from data.
runge_kutta_method
Macro to create a Runge-Kutta solver from a Butcher tableau with fixed-size arrays
vector
Construct a fixed-size column vector directly from data.

Type Aliases§

SMatrix
A statically sized column-major matrix with R rows and C columns.
SVector
A statically sized D-dimensional column vector.