Abstract
A discretization algorithm for initial boundary-value problems is developed for systems of two linear equations of hyperbolic type with discontinuous solutions. A Crank—Nicholson scheme is constructed for discretization of the Cauchy problem and error bounds are obtained for the approximate solution. A model example is solved.
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References
V. S. Deineka, "Determination of discontinuous characteristics of rods with inclusions," Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 9, 20–24 (1987).
V. S. Deineka and I. N. Molchanov, "Finite-element schemes for problems of elasticity theory," Zh. Vychisl. Mat. Mat. Fiz.,21, No. 2, 452–469 (1981).
O. C. Zienkiewicz, Finite Element Method in Engineering Science, McGraw-Hill, New York (1971).
I. I. Lyashko, V. V. Skopet'skii, and V. S. Deineka, "Numerical discretization of a homogeneous nonlinear equation of parabolic type with discontinuous solutions," Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 5, 20–24 (1987).
I. N. Molchanov, Computer Methods of Solving Applied Problems. Differential Equations [in Russian], Kiev (1988).
A. Garth and F. Baker, "Error estimates for finite-element methods for second-order hyperbolic equations," SIAM J. Numer. Anal.13, No. 4, 564–576 (1976).
Additional information
Institute of Cybernetics of the Ukrainian Academy of Sciences. Kiev University. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 75, pp. 75–83, 1991.
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Skopetskii, V.V., Deineka, V.S. & Marchenko, O.A. Discretization of the dynamic problem of elasticity theory with a discontinuous solution. J Math Sci 72, 3109–3115 (1994). https://doi.org/10.1007/BF01259481
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DOI: https://doi.org/10.1007/BF01259481