Numerical solution of a time-optimal parabolic boundary-value control problem

A special time-optimal parabolic boundary-value control problem describing a one-dimensional heat-diffusion process is solved numerically. Using a bang-bang principle recently proved by Lempio, this problem can be transformed in such a way that the variables are jumps of bang-bang controls. A discretization is performed in two steps, and the convergence of the approximate solutions is proved. Finally, an algorithm to solve the discrete problem is developed and some numerical results are discussed.The author would like to thank Prof. F. Lempio, who pointed out this problem to him, and Prof. K. Glashoff for many helpful comments and suggestions.