Cubic Spline Quadrature
Source inspiration: (Mathew 2000-2019).
Animations
Each animation below shows the cubic spline quadrature diagram building up panel by panel over \([0, 2]\) for \(y = e^{-x}\sin(8x^{2/3})+1\). Each frame adds one new spline panel. A natural cubic spline is first fitted through all \(n+1\) nodes, then each sub-interval is integrated exactly (using the cubic polynomial coefficients). The dashed blue curve shows the cumulative spline approximation.
Julia source scripts that generated these animations are linked under each case.
Case 1 — Natural Cubic Spline Quadrature, \(y = e^{-x}\sin(8x^{2/3})+1\), \(n=10\)
Behavior: The natural cubic spline interpolates all \(n+1\) nodes globally, then each sub-interval is integrated exactly. This is more accurate than Simpson’s rule for smooth functions since the cubic spline has \(O(h^4)\) interpolation error with a smaller constant.
Derivation Notes (Planned)
Short derivations will be added to explain the core equations and assumptions.
Worked Example (Planned)
A compact numerical example with intermediate steps will be included.
Implementation Notes (Planned)
Implementation details, numerical stability notes, and practical pitfalls will be added.
Legacy Animation Inventory (Stub)
- Legacy module page: Cubic Spline Quadrature (ok)
- Animation links found in module Animations paragraph: 4
- Unique animation portals: 1
Animation Portals
- Animation item links found: 1
Animation Items
- Main animated GIF count: 1
- http://localhost:8000/a2001/Animations/Quadrature/Spline/Splineaa.gif