Regularization of the Solution of a Cauchy Problem for a Hyperbolic Equation

Given a hyperbolic equation with variable coefficients, we construct a regularizingalgorithm to solve the problem of continuation of the wave field from the boundary of thehalf-plane inside it. We introduce some N-approximatesolutions and establish their convergence to the exact solution. Under consideration is the casewhen the problem data have an error of δ. We find anestimate of the accuracy of the approximate solutions and prove the convergence of theapproximate solutions to the unique solution as δ→0.