Title data
Grüne, Lars ; Le, Thuy Thi Thien:
A new approach to the minimum time problem and its numerical approximation.
Department of Mathematics, University of Bayreuth
Bayreuth
,
2015
.  17 S.
PDF
Gruene_et_al_new_approach_min_time_prob_2015.pdf  Preprint Available under License Deutsches Urheberrechtsgesetz . Download (1MB) 
Project information
Project title: 



Project financing: 
Andere Fondazione CARIPARO 
Abstract
We introduce a new formulation of the minimum time problem in which we employ the signed minimum time function positive outside of the target, negative in its interior and zero on its boundary. Under some standard assumptions, we prove the so called Bridge Dynamic Programming Principle (BDPP) which is a relation between the value functions defined on the complement of the target and in its interior. Then owing to BDPP, we obtain the error estimates of a semiLagrangian discretization of the resulting HamiltonJacobiBellman equation. In the end, we provide numerical tests and error comparisons which show that the new approach can lead to significantly reduced numerical errors.