Abstract A phase-fitting approach allows vanishing for not only the phase lag but also its first, second, third, fourth, fifth, and sixth derivatives to be considered. The new technique is dubbed economical method because it uses the maximum possible algebraic order (AOR) while simultaneously performing the fewest possible function evaluations (FEvs). The formula for this innovative method is PF6DPFN2SPS. The proposed technique is P-Stable (i.e. infinitely periodic).