LINEAR LAVRENT'EV INTEGRAL EQUATION FOR THE NUMERICAL SOLUTION OF A NONLINEAR COEFFICIENT INVERSE PROBLEM

For the first time, we develop a convergent numerical method for the linear integral equation derived by M.M. Lavrent'ev in 1964 with the goal of solving a coefficient inverse problem for a wavelike equation in 3 dimensions. The data are non overdetermined. Convergence analysis is presented along with the numerical results. An intriguing feature of the Lavrent'ev equation is that, without any linearization, it reduces a highly nonlinear coefficient inverse problem to a linear integral equation of the first kind. Nevertheless, numerical results for that equation, which use the data generated for that coefficient inverse problem, show a good reconstruction accuracy. This is similar with the classical Gelfand-Levitan equation derived in 1951, which is valid in the 1 dimensional case.