centered_8th_deriv_uniform

Family: finite_difference
Grid family: cartesian
Kind: scheme
Accuracy: O(dx^8)
Applies to: d2($u), dim=$x
Rule file: discretizations/finite_difference/centered_8th_deriv_uniform.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 d2 on the pattern d2($u), dim=$x 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):

out[$x] = (8064·(index($u, $x − 1) + index($u, $x + 1)) − 1008·(index($u, $x − 2) + index($u, $x + 2)) + 128·(index($u, $x − 3) + index($u, $x + 3)) − 9·(index($u, $x − 4) + index($u, $x + 4)) − 14350·index($u, $x))/(5040·dx·dx)

Source: discretizations/finite_difference/centered_8th_deriv_uniform.json.