An Effective Computational Scheme for the Optimal Control of Wave Equations

With a standard second-order central finite difference scheme in space, the full discretization is proved to be unconditionally convergent with a second-order accuracy. Moreover, based on its favorable structure, an efficient preconditioned iterative method is provided for solving the discretized unsymmetric sparse linear system. Numerical examples are presented to confirm our theoretical conclusions and demonstrate the promising performance of our proposed algorithms.