Interval polynomial enclosure

[schillic]

An old ODE/IVP solution approach based on interval arithmetic is outlined in Introduction to interval analysis, Section 10.2, or in A brief introduction to interval analysis, p. 191f. The idea is to compute an interval polynomial (a polynomial with interval coefficients) that looks similar to a Taylor polynomial. The result is a sound overapproximation of the actual ODE solution.

As I understand it, all that is required is symbolic integration of polynomials, which is (conceptually) simple. I am not sure if this holds for non-polynomial ODEs, though.

This is orthogonal to JuliaReach/Reachability.jl#164.