Bounding the Solutions of Parametric ODEs When Taylor Models Meet Differential Inequalities

This article presents a new method for computing Taylor models of the solutions of parametric ODEs, based on the theory of differential inequalities. Rather than bounding the solutions directly using interval analysis, the idea is to bound the remainder term in a Taylor series expansion of these solutions, which leads to a high-order convergence rate. A practical procedure for propagating the Taylor model estimators over a given time horizon is described. The methodology is illustrated by the case study of a Lotka-Volterra system.