Abstract
In this paper we consider a numerical solution of the non-classical Dirichlet problem and its modifications for the second-order two-dimensional hyperbolic equations. In order to determine the missing initial condition using an additional condition specified at the final time, an iterative method of conjugate gradient is used. A direct problem is numerically realized at each iteration. The efficiency of the proposed computational algorithm is confirmed by calculations for model two-dimensional problems.
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Acknowledgments
Supported by mega-grant of the Russian Federation Government (14.Y26.31.0013) and Grant of the Russian Foundation for Basic Research (17-01-00732).
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Vasil’ev, V.I., Kardashevsky, A.M., Popov, V.V. (2019). The Conjugate Gradient Method for the Dirichlet Problem and Its Modifications. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Finite Difference Methods. Theory and Applications. FDM 2018. Lecture Notes in Computer Science(), vol 11386. Springer, Cham. https://doi.org/10.1007/978-3-030-11539-5_69
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DOI: https://doi.org/10.1007/978-3-030-11539-5_69
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