neco-dop853

Adaptive Dormand-Prince 8(5,3) integration for ordinary differential equations on slice-based state vectors.

Integration model

integrate_dop853 advances an explicit ODE system on &[f64] state vectors and samples the solution at the requested t_eval points.

The solver uses adaptive step control internally, but the returned Dop853Result stays small: sampled times, sampled states, and a success flag.

Usage

use neco_dop853::{integrate_dop853, Dop853Options};

let rhs = |_t: f64, y: &[f64], dydt: &mut [f64]| {
    dydt[0] = -y[0];
};

let t_eval = [0.0, 0.5, 1.0, 2.0];
let result = integrate_dop853(
    rhs,
    (0.0, 2.0),
    &[1.0],
    &t_eval,
    &Dop853Options::default(),
);

assert!(result.success);
assert_eq!(result.t, t_eval);
assert!((result.y[3][0] - (-2.0f64).exp()).abs() < 1e-10);

API

Item	Description
`integrate_dop853(rhs, t_span, y0, t_eval, opts)`	Integrate an explicit ODE system and sample the solution at the requested times
`Dop853Options`	Relative tolerance, absolute tolerance, maximum step, and an `initial_step` hint (`0.0` means automatic choice)
`Dop853Options::default()`	Conservative defaults for high-accuracy forward integration
`Dop853Result`	Returned sample times, sampled states, success flag, accepted step count, and RHS evaluation count
`Dop853Result::success`	`true` when the solver reaches every requested `t_eval` point before hitting the internal stop conditions

Preconditions

rhs must write one derivative value per state entry into dydt.
t_eval is expected to be monotonically nondecreasing and to stay within t_span.
The current implementation targets forward integration (t_span.0 <= t_span.1).
Sample points exactly at t_span.0 are returned as the initial state without advancing the solver.
Intermediate t_eval points are reconstructed with Hermite cubic interpolation between accepted steps.
If the solver cannot reach every requested output time, it returns the partial output it has accumulated and sets success to false.

Failure semantics

This crate currently reports integration failure through Dop853Result::success instead of Result.

Typical success = false cases:

some requested t_eval values lie beyond the reachable part of t_span
the adaptive step size shrinks below the internal minimum threshold
the solver hits the internal step cap before consuming all requested outputs

License

MIT