Boole’s Rule
Source inspiration: (Mathew 2000-2019).
Animations
Each animation below shows the Boole’s rule diagram building up panel by panel over \([0, 2]\) for \(y = e^{-x}\sin(8x^{2/3})+1\). Each frame adds one new Boole panel (spanning 4 subintervals = 5 nodes); the running sum is annotated. Boole’s rule fits a 4th-degree polynomial through 5 nodes — achieving \(O(h^6)\) accuracy.
Julia source scripts that generated these animations are linked under each case.
Case 1 — Boole’s Rule, \(y = e^{-x}\sin(8x^{2/3})+1\), \(n=8\) subintervals
Behavior: Each panel uses 5 nodes and the formula \(\frac{2h}{45}(7f_0 + 32f_1 + 12f_2 + 32f_3 + 7f_4)\). Boole’s rule is exact for polynomials up to degree 5, giving \(O(h^6)\) accuracy — the highest of the Newton–Cotes family shown here.
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: Boole’s Rule (ok)
- Animation links found in module Animations paragraph: 4
- Unique animation portals: 1
Animation Portals
- Boole’s Rule (ok)
- Animation item links found: 1
Animation Items
- Boole’s Rule (ok)
- Main animated GIF count: 1
- http://localhost:8000/a2001/Animations/Quadrature/Boole/Booleaa.gif