Numerical Mathematics and Control

Discrete Mathematics , Discrete Physics and Numerical Methods ∗

Discrete mathematics has been neglected for a long time. It has been put in the shade by the striking success of continuous mathematics in the last two centuries, mainly because continuous models in physics proved very reliable, but also because of the greater difficulty in dealing with it. This perspective has been rapidly changing in the last years owing to the needs of the numerical analysis...

Wave Equation Numerical Resolution: Mathematics and Program

We formally prove the C program that implements a simple numerical scheme for the resolution of the one-dimensional acoustic wave equation. Such an implementation introduces errors at several levels: the numerical scheme introduces method errors, and the floating-point computation leads to round-off errors. We formally specify in Coq the numerical scheme, prove both the method error and the rou...

Numerical Mathematics ? ? ( 199 ? ) , ? { ? Highly Stable ParallelRunge - Kutta

The construction of stiiy accurate and B-stable multi-implicit Runge-Kutta methods for parallel implementation is discussed. A fth and a seventh order method is constructed and a promising numerical comparison with the eecient Radau5 code of E. Hairer and G. Wanner is conducted.

Pacific Journal of Mathematics IRREDUCIBLE NUMERICAL SEMIGROUPS

36th Northern German Colloquium on Applied Analysis and Numerical Mathematics

Alessandro Alla (Universität Hamburg) Talk: Coupling MPC and DP methods for optimal control problems We consider the approximation of an infinite horizon optimal control problem which combines a first step based on Model Predictive Control (MPC) in order to have a quick guess of the optimal trajectory and a second step where we solve the Bellman equation in a neighborhood of the reference traje...