Abstract. This work focuses on numerical solutions
of optimal control problems. A time discretization error representation
is derived for the approximation of the associated value function. It
concerns Symplectic Euler solutions of the Hamiltonian system connected
with the optimal control problem. The error representation has a leading
order term consisting of an error density that is computable from
Symplectic Euler solutions. Under an assumption of the pathwise
convergence of the approximate dual function as the maximum time step
goes to zero, we prove that the remainder is of higher order than the
leading error density part in the error representation. With the error
representation, it is possible to perform adaptive time stepping. We
apply an adaptive algorithm originally developed for ordinary di
erential equations. The performance is illustrated by numerical tests.