Standard-Slope Integration (SSI)

Standard‑Slope Integration (SSI) is a numerical integration framework that operates directly on slope‑defined systems, using derivative information as the primary computational object. Instead of advancing a solution through step‑based accumulation, SSI reconstructs system behavior through slope‑based reconstruction and structural iteration invariants, producing a stable, derivative‑driven integration operator with predictable and analytically transparent behavior.

Classical integrators accumulate local truncation error at each step, and their stability depends on step size, conditioning, and error‑control heuristics. SSI avoids this step‑accumulation model entirely. By constructing a globally coherent slope‑field representation, the method remains stable under refinement; increasing resolution improves accuracy without the instability or drift seen in classical step‑based methods, even in stiff or irregular regimes.

This project presents the mathematical formulation of SSI, its motivation as a new class of derivative‑driven integration operators, and its practical implementation. Additional examples, analysis, and source code are provided in the repository and documentation.

A slope‑based integration operator that defines integrals without antiderivatives.

The full definition, examples, and citation details are in the project README.
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