Crate numra_dde 

DDE (Delay Differential Equation) solvers for Numra.

This crate provides methods for solving delay differential equations of the form:

y'(t) = f(t, y(t), y(t - τ₁), y(t - τ₂), ...)

where τᵢ are the delays (constant or state-dependent).

Solvers

• MethodOfSteps - Method of steps using embedded RK solver

Example

use numra_dde::{DdeSystem, MethodOfSteps, DdeSolver, DdeOptions};

// Mackey-Glass equation: y'(t) = β * y(t-τ) / (1 + y(t-τ)^n) - γ * y(t)
struct MackeyGlass {
    beta: f64,
    gamma: f64,
    n: f64,
    tau: f64,
}

impl DdeSystem<f64> for MackeyGlass {
    fn dim(&self) -> usize { 1 }
    fn delays(&self) -> Vec<f64> { vec![self.tau] }
    fn rhs(&self, _t: f64, y: &[f64], y_delayed: &[&[f64]], dydt: &mut [f64]) {
        let y_tau = y_delayed[0][0];  // y(t - tau)
        dydt[0] = self.beta * y_tau / (1.0 + y_tau.powf(self.n)) - self.gamma * y[0];
    }
}

let mg = MackeyGlass { beta: 2.0, gamma: 1.0, n: 9.65, tau: 2.0 };
let history = |_t: f64| vec![0.5];  // Constant history
let opts = DdeOptions::default();
let result = MethodOfSteps::solve(&mg, 0.0, 100.0, &history, &opts);

Author: Moussa Leblouba Date: 3 February 2026 Modified: 2 May 2026

Structs

DdeOptions

Options for DDE solvers.

DdeResult

Result of DDE integration.

DdeStats

Statistics from DDE solver.

HermiteInterpolator

Hermite cubic interpolator for a single step.

History

History storage for DDE solver.

MethodOfSteps

Method of Steps DDE solver.

Traits

DdeSolver

Trait for DDE solvers.

DdeSystem

Trait for delay differential equation systems.

HistoryFunction

Trait for history functions.

Scalar

A real scalar type suitable for numerical computation.