Abstract
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 \(\delta \to 0\).
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The authors were supported by the State Task to the Sobolev Institute of Mathematics (project no. 0314–2019–0011).
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Translated by L.B. Vertgeim
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Romanov, V.G., Bugueva, T.V. & Dedok, V.A. Regularization of the Solution of a Cauchy Problem for a Hyperbolic Equation. J. Appl. Ind. Math. 15, 118–128 (2021). https://doi.org/10.1134/S1990478921010105
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DOI: https://doi.org/10.1134/S1990478921010105