A Legendre Galerkin spectral method for optimal control problems

This paper considers the Legendre Galerkin spectral approximation for the unconstrained optimal control problems. The authors derive a posteriori error estimate for the spectral approximation scheme of optimal control problem. By choosing the appropriate basis functions, the stiff matrix of the discretization equations is sparse. And the authors use the Fast Legendre Transform to improve the efficiency of this method. Two numerical experiments demonstrating our theoretical results are presented.