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Operator Splitting for Quasi-Linear Abstract Hyperbolic Equation

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Abstract

We consider an abstract hyperbolic equation with a Lipschitz continuous operator, where the main operator is self-adjoint and positive definite and represents a sum of two similar operators. For this equation, we construct a decomposition scheme of high order of accuracy. This scheme is based on rational splitting of cosine-operator function.

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Author information

Authors and Affiliations

  1. Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia

    N. Dikhaminjia & J. Rogava

  2. I. Vekua Institute of Applied Mathematics, Tbilisi, Georgia

    N. Dikhaminjia & J. Rogava

  3. EMC Laboratory, Missouri University of Science & Technology, Rolla, Missouri, USA

    M. Tsiklauri

Authors
  1. N. Dikhaminjia
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  2. J. Rogava
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  3. M. Tsiklauri
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Corresponding author

Correspondence to J. Rogava.

Additional information

Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 97, Proceedings of the International Conference “Lie Groups, Differential Equations, and Geometry,” June 10–22, 2013, Batumi, Georgia, Part 2, 2015.

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Dikhaminjia, N., Rogava, J. & Tsiklauri, M. Operator Splitting for Quasi-Linear Abstract Hyperbolic Equation. J Math Sci 218, 737–741 (2016). https://doi.org/10.1007/s10958-016-3058-9

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  • DOI: https://doi.org/10.1007/s10958-016-3058-9

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