2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/205699We describe a modification of a fourth-order accurate ``moving puncture'' evolution code, where by replacing spatial fourth-order accurate differencing operators in the bulk of the grid by a specific choice of sixth-order accurate stencils we gain significant improvements in accuracy. We illustrate the performance of the modified algorithm with an equal-mass simulation covering nine orbits.13 pages, 6 figuresGeneral Relativity and Quantum Cosmologytext