Regularization of the solution of a Cauchy problem for a hyperbolic equation

Given a hyperbolic equation with variable coefficients, we construct a regularizing algorithm to solve the problem of continuation of the wave field from the boundary of the half-plane inside it. We introduce some $N$-approximate solutions and establish their convergence to the exact solution. Under consideration is the case when the problem data have an error of $\delta$. We find an estimate of the accuracy of the approximate solutions and prove the convergence of the approximate solutions to the unique solution as $\delta \to 0$.