#standardslopeintegration — Public Fediverse posts

Start here: Standard-Slope Integration (SSI)

A new, first-of-its-kind class of derivative-driven integration operators built solely from slope information.

If you’re new to my work, this post links to the full SSI series—a structured overview of a first-of-its-kind, derivative-driven integration operator built on structural iteration invariants and slope-based reconstruction. The recap summarizes all seven posts in order and provides the conceptual foundation for understanding SSI.

Series recap:

https://mathstodon.xyz/@BlueNovaX/116523359117197532

Repository with details and examples:

https://github.com/BlueNovaX/standard-slope-integration

#numericalanalysis #scientificcomputing #mathematics #integration #StandardSlopeIntegration #SSI

Standard‑Slope Integration (SSI) — Post #3: Failure-mode robustness

A new, first-of-its-kind class of derivative-driven integration operators built solely from slope information.

Classical integration methods often fail when the integrand is discontinuous, poorly conditioned, or structurally misaligned with area-based accumulation. SSI approaches these cases differently: its derivative-driven structure and step-to-step invariants prevent the amplification and drift that destabilize classical formulations.

This makes SSI effective in cases where traditional quadrature becomes unstable, unreliable, or fails outright—not by modifying classical methods, but by using a fundamentally different reconstruction principle.

#numericalanalysis #scientificcomputing #mathematics #integration #StandardSlopeIntegration #SSI