解一类最优控制问题的勒让德伽略金方法

In this paper, an efficient Legendre Galerkin method for the optimal control problems without constraints is considered. By choosing the appropriate basis functions, the stiff matrix of the discretization equations is sparse. And the efficiency of the algorithm is improved by using fast Legendre transform. Then two numerical experiments of the one dimensional and two dimensional respectively are presented to confirm the error estimates.