Module calculus 

Calculus & Differential Solvers - Zero-Allocation Implementation

This module provides fixed-size stack-based solvers for differential equations, boundary value problems, and numerical integration suitable for the #![no_std] environment of Qualia-DB.

Modules

analysis

Finite-dimensional analysis foundations used by native calculus.

capabilities

Machine-readable capability truth for the native calculus surface.

dense

General-dimension numerical methods (Calculus plan §4.4).

differential

Numerical and automatic differential calculus.

exterior

Bounded exterior algebra for three-dimensional calculus and geometry.

grid

Continuous-grid numerical integration — Simpson / trapezoidal rules (Kahan- compensated, SIMD-accelerated chunking) over zero-copy mmap-backed f64 grids, plus the DMA-alignment / state-suspension helpers. Relocated here from modalities::calculus as STEM math; the VM opcode surface that dispatches these stays in modalities::calculus (the modality), the numbers live in the solver.

manifold

Finite-dimensional chart and Riemannian metric primitives.

mechanics

Hamiltonian mechanics primitives with invariant diagnostics.

ode_adaptive

Caller-buffered adaptive Dormand-Prince ODE integration.

ode_advanced

Advanced ODE integrators: symplectic, stiff (BDF), dense output, and forward sensitivity — the doctorate-level capabilities the ode_solver scalar RK4/BVP core does not provide.

ode_solver

ODE Solver for coupled differential equations

potential

Bounded finite-difference potential solver.

quadrature

Adaptive scalar quadrature with bounded, non-recursive work stacks.

tensor_integrity

Tamper-evident, append-only lineage commitments for tensor provenance, plus a zero-knowledge binding to verified linear-transformation proofs.

tensor_provenance

Tensor Provenance Tracking

workspace

Caller-owned calculus workspace accounting.

Structs

BVPState

BVP state for shooting method

IntegralChunk

Integral chunk for processing

ODEState

ODE state for RK4 solver

RungeKutta4Static

Runge-Kutta 4th order ODE solver with fixed memory footprint

ShootingMethodBVP

Boundary Value Problem solver using shooting method

SimpsonsIntegratorChunked

Simpson’s rule integrator with chunked processing

Traits

BVPFunction

BVP function trait for shooting method

IntegrandFunction

Integrand function trait for Simpson’s integrator

ODEFunction

ODE function trait for RK4