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FIX: Correct adaptive step size exponent for embedded RK methods #91

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Merged
Axect merged 1 commit into from
Feb 6, 2026
Merged

FIX: Correct adaptive step size exponent for embedded RK methods #91

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22 changes: 16 additions & 6 deletions src/numerical/ode.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -290,6 +290,12 @@ pub trait ButcherTableau {
fn max_step_iter(&self) -> usize {
unimplemented!()
}

/// Order of the lower-order solution for adaptive step size control.
/// The exponent `1/(order+1)` is used in the step size formula.
fn order(&self) -> usize {
4
}
}

impl<BU: ButcherTableau> ODEIntegrator for BU {
Expand Down Expand Up @@ -324,7 +330,7 @@ impl<BU: ButcherTableau> ODEIntegrator for BU {
error = error.max(dt * s.abs())
}

let factor = (self.tol() / error).powf(0.2);
let factor = (self.tol() / error).powf(1.0 / (self.order() as f64 + 1.0));
let new_dt = self.safety_factor() * dt * factor;
let new_dt = new_dt.clamp(self.min_step_size(), self.max_step_size());

Expand Down Expand Up @@ -558,6 +564,9 @@ impl ButcherTableau for BS23 {
fn max_step_iter(&self) -> usize {
self.max_step_iter
}
fn order(&self) -> usize {
2
}
}

/// Runge-Kutta-Fehlberg 4/5th order integrator.
Expand Down Expand Up @@ -1098,9 +1107,7 @@ impl ButcherTableau for RKF78 {
],
];

// Coefficients for the 7th order solution (propagated solution)
// BU_i = BE_i (8th order) - ErrorCoeff_i
// ErrorCoeff_i = [-41/840, 0, ..., 0, -41/840 (for k11), 41/840 (for k12), 41/840 (for k13)]
// Coefficients for the 8th order solution (propagated via local extrapolation)
const BU: &'static [f64] = &[
0.0,
0.0,
Expand All @@ -1117,8 +1124,8 @@ impl ButcherTableau for RKF78 {
41.0 / 840.0,
];

// Coefficients for the 8th order solution (used for error estimation)
// These are from the y[i+1] formula in the MATLAB description
// Synthetic coefficients for error estimation
// BU - BE yields the Fehlberg error formula: 41/840 * (k1 + k11 - k12 - k13)
const BE: &'static [f64] = &[
41.0 / 840.0,
0.0,
Expand Down Expand Up @@ -1150,6 +1157,9 @@ impl ButcherTableau for RKF78 {
fn max_step_iter(&self) -> usize {
self.max_step_iter
}
fn order(&self) -> usize {
7
}
}

// ┌─────────────────────────────────────────────────────────┐
Expand Down