This　paper　focuses　on　the　error　analysis　of　a　first-order,　time-discrete　scheme　for　solving　the　nonlinear　Allen–Cahn　equation.　The　discretization　of　the　nonlinear　potential　is　achieved　through　the　EIEQ　method,　which　employs　an　auxiliary　variable　to　linearize　the　nonlinear　double-well　potential　effectively.　The　energy　stability　of　the　scheme　is　demonstrated,　along　with　its　decoupled　type　implementation.　Under　a　set　of　reasonable　assumptions　related　to　boundedness　and　continuity,　an　extensive　error　analysis　is　performed.　This　analysis　results　in　the　establishment　of　L2　and　H1　error　bounds　for　the　numerical　solution.　Furthermore,　a　variety　of　numerical　examples　are　conducted　to　illustrate　the　accuracy　of　the　EIEQ　scheme,　highlighting　its　effectiveness　in　addressing　complex　dynamical　systems　governed　by　the　Allen–Cahn　equation.　©　2024　Elsevier　B.V.