numra-ide

Volterra integro-differential equation solvers for the Numra workspace — general quadrature solver plus a Prony-series fast path for exponential kernels.

Solves Volterra IDEs y'(t) = f(t, y) + ∫₀ᵗ K(t, s, y(s)) ds for history-dependent dynamics. The general VolterraSolver handles arbitrary memory kernels via quadrature; the specialized PronySolver exploits sums of exponentials for an O(N) rather than O(N²) step cost.

Example

use numra_ide::kernels::ExponentialKernel;
use numra_ide::{IdeOptions, IdeSolver, IdeSystem, Kernel, VolterraSolver};

// Viscoelastic: y' = -k·y + ∫ K(t-s)·y(s) ds with exponential kernel
struct Viscoelastic {
    k: f64,
    kernel: ExponentialKernel<f64>,
}

impl IdeSystem<f64> for Viscoelastic {
    fn dim(&self) -> usize { 1 }
    fn rhs(&self, _t: f64, y: &[f64], f: &mut [f64]) {
        f[0] = -self.k * y[0];
    }
    fn kernel(&self, t: f64, s: f64, y: &[f64], k: &mut [f64]) {
        k[0] = self.kernel.evaluate(t - s) * y[0];
    }
}

What's in this crate

Solvers:

• VolterraSolver — general Volterra IDE solver using quadrature
• VolterraRK4Solver — RK4-based variant
• PronySolver — O(N) fast path for sum-of-exponentials kernels via Prony reduction

Kernels:

• ExponentialKernel — K(t, s) = a · exp(-b(t-s))
• PowerLawKernel — K(t, s) = (t-s)^{-α}, fractional memory
• PronyKernel — sum-of-exponentials representation
• Kernel trait — user-defined kernels

Composes with

• numra-fde — power-law kernels share the long-memory machinery of fractional derivatives
• numra-interp for post-hoc resampling of viscoelastic relaxation curves
• numra-fit for fitting Prony coefficients to measured kernel responses

See cross-formalism tests for IDE-reduces-to-ODE consistency and memory-kernel composition.

Install

[dependencies]
numra-ide = "0.1"

Or via the umbrella crate:

[dependencies]
numra = "0.1"

Documentation

• API: https://docs.rs/numra-ide
• Book: Integro-DEs
• Source: https://github.com/moussaoutlook/numra-rs/tree/main/numra-ide

License

Numra Academic & Research License (Non-Commercial). Academic and research use is free; commercial use requires a separate license — contact contact@spectralautomata.com. See LICENSE.