On Vergnaud's time integration method for autocatalytic cure rate equations

A hybrid numerical-analytical scheme for time integration of the cure rate equation, governing the autocatalytic cure reaction of epoxy resins, is presented. The method is an extension of Vergnaud's approach for the integration of heterocatalytic cure reactions of epoxy resins. It is applicable to first order, semi-linear, ordinary differential equations with separated variables, where the integration of the dependent variable can be obtained analytically. Numerical quadrature is used for the integration of the independent variable, which appears in a time-dependent integral of an Arrhenius term containing temperature. Consistency and L-stability of the method are proved and some error estimates are provided. Several numerical results validate the high accuracy of the proposed integration scheme.