In this paper,optimize-then-discretize,variational discretization and the finite volume method are applied to solve the distributed optimal control problems governed by a second order hyperbolic equation.A semi-discrete optimal system is obtained.We prove the existence and uniqueness of the solution to the semidiscrete optimal system and obtain the optimal order error estimates in L ∞(J;L 2)-and L ∞(J;H 1)-norm.Numerical experiments are presented to test these theoretical results.
We propose and analyze a spectral Jacobi-collocation approximation for fractional order integro-differential equations of Volterra type. The fractional derivative is described in the Caputo sense. We provide a rigorous error analysis for the collection method, which shows that the errors of the approximate solution decay exponentially in L^∞ norm and weighted L^2-norm. The numerical examples are given to illustrate the theoretical results.
