Title: A Posteriori Error Analysis of a Non-Standard Quantity of Interest

Abstract: Classical a posteriori error analysis quantifies error in a Quantity of Interest (QoI) which is represented as a bounded linear functional of the solution.  In this work we consider a posteriori error estimates of a specified non-linear quantity of interest using adjoint-based analysis for linear and nonlinear systems of Ordinary Differential Equations.  We derive two methods for computing such error estimates.  The first directly computes the error estimate using linearizations via Taylor’s  Theorem.   The  second  method  acquires  our  estimate  indirectly  by  implementing  root-finding techniques on a corrected solution.  We provide several examples to test the accuracy of the methods.