Symbolic and Numeric Computation of Optimal Initial Velocity in a Wave Equation

Abstract

We get symbolic and numeric solutions developing a MAPLEآ® program which uses the initial velocity on the state variable of a wave equation as control function. Solution of this problem implies the minimization at the final time of the distance measured in a suitable norm between the solution of the problem and a given target. An iterative algorithm is constructed to compute the required optimal control as the limit of a suitable subsequence of controls. Results are tested with some numerical examples.