DIY
Stump burning
Stump burning is burning a stump out in place. University of Illinois Extension says to check local ordinances first, and Iowa State Extension lists burning as a method to avoid.
University of Illinois Extension says stumps can be burned out, but to check local ordinances to see whether open burning is permitted. It adds that a stump fire will burn hot and possibly for many days, and that high heat can sterilize the surrounding soil.
Iowa State Extension puts burning first on its list of methods not recommended. It says accelerants such as diesel fuel can leach into soil and are highly flammable and dangerous, and that many cities and counties do not allow burning. This page does not give burning steps. Safer options include stump grinding and digging out a stump. The guide on burning a tree stump has the full comparison.