Convergence results for simplicia1 fixed point algorithms applied to problems in Banach-spaces enable constructive proofs of the existence of fixed points for set valued operators [14]. Boundary value problems for differential inclusions will be interpreted in this context. The resulting new algorithm allows numerical treatment of boundary value problems with Peano-typedynamics. The necessary conditions of the Pontryagin Maximum Principle are discussed in this framework, leading to a new indirect method for the computation of optimal trajectories with its focus on global convergence conditions for compact control domains.