Imperial–UCL Numerics Seminar

Abstract:

In computer-aided mathematical proofs, a basic, yet critical, building block is the problem of actually obtaining numerical values. In practice, one strives to achieve precise and/or guaranteed results without compromising efficiency. For this, we combine symbolic and numerical computation, which leads to the development of specific approximation algorithms. In this talk, we present an efficient validated numerics method for solving linear ordinary differential equations (LODEs) in terms of truncated Chebyshev series together with rigorously computed error bounds. Our approach is illustrated by validating solutions of fuel-optimal impulsive control problems  for rendezvous between spacecraft. This is joint work with D. Arzelier, F.

Brehard and N. Brisebarre.