Dynamical inverse problem on a metric tree

Abstract

We consider the problem of reconstruction of the potential for the wave equation on a specific star graph using the dynamical Dirichlet-to-Neumann map. Our algorithm is based on the boundary control method. We reduce the problem of reconstruction to a second kind Fredholm integral equation, the kernel and the right-hand side of which arise from an auxiliary second kind Volterra integral equation. A second-order accurate numerical method for the equations is described and implemented. Then several numerical examples demonstrate that the algorithm works and can be used to reconstruct an unknown potential accurately.