midpoint_1d

Family: integral
Grid family: cartesian
Kind: scheme
Accuracy: O(h^2) midpoint/Euler quadrature of a full-domain 1-D integral on a uniform cartesian grid
Applies to: integral($u)
Rule file: discretizations/integral/midpoint_1d.json

This page is auto-generated from the rule's JSON by tools/render_doc_plots.py. The discrete operator below is pretty-printed directly from the rule's replacement AST using EarthSciSerialization (earthsci_toolkit). Rules with a hand-authored page carry richer prose plus stencil and convergence diagrams; see the curated entries linked from the rule index.

Pattern

Matches the §4.2 operator integral on the pattern integral($u) for grid family cartesian.

Discrete operator

Pretty-printed from the rule’s replacement AST ($-prefixed names are pattern variables bound by applies_to; grid metrics such as dx/dz are resolved by the grid):

dx·arrayop(size_x)

Source: discretizations/integral/midpoint_1d.json.