A numerical algorithm for solving an inverse semilinear wave problem (Q2341493)

Summary: The problem of identifying the solution \((k(x, t),U(x, t))\) in an inverse semilinear wave problem is considered. It is shown that under certain conditions of data \(\phi\), \(\psi\), there exists a unique solution \((k(x, t),U(x, t))\) of this problem. Furthermore a numerical algorithm for solving the inverse semilinear wave problem is proposed. The approach for this inverse problem is given by using the semi-discretisation method. A polynomial function is proposed to approximate \(U(x, t)\) then the finite difference method is applied to approximate unknown \(k(x, t)\). Numerical results show efficiency of our method.