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Operator-Difference Scheme with a Factorized Operator

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Large-Scale Scientific Computing (LSSC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9374))

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Abstract

In the study of difference schemes for time-dependent problems of mathematical physics, the general theory of stability (well-posedness) for operator-difference schemes is in common use. At the present time, the exact (matching necessary and sufficient) conditions for stability are obtained for a wide class of two- and three-level difference schemes considered in finite-dimensional Hilbert spaces.

The main results of the theory of stability for operator-difference schemes are obtained for problems with self-adjoint operators. In this work, we consider difference schemes for numerical solution of the Cauchy problem for first order evolution equation, where non-self-adjoint operator is represented as a product of two non-commuting self-adjoint operators. We construct unconditionally stable regularized schemes based on the solution of a grid problem with a single operator multiplier on the new time level.

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References

  1. Samarskii, A.A.: The Theory of Difference Schemes. Marcel Dekker, New York (2001)

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  2. Samarskii, A.A., Gulin, A.V.: Stability of Difference Schemes. URSS, Moscow (2004). In Russian

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  3. Samarskii, A.A., Matus, P.P., Vabishchevich, P.N.: Difference Schemes with Operator Factors. Springer, Dordrecht (2002)

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Acknowledgements

This work was supported by RFBR (project 14-01-00785)

Author information

Authors and Affiliations

  1. Nuclear Safety Institute, 52, B. Tulskaya, 115191, Moscow, Russia

    Petr N. Vabishchevich

  2. North-Eastern Federal University, 58, Belinskogo, 677000, Yakutsk, Russia

    Petr N. Vabishchevich

Authors
  1. Petr N. Vabishchevich
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Correspondence to Petr N. Vabishchevich .

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Editors and Affiliations

  1. Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Lirkov

  2. Inst. of Inform. & Communication, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Svetozar D. Margenov

  3. Informatics and Mathematical Modell, Technical University of Denmark, Kongens Lyngby, Denmark

    Jerzy Waśniewski

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© 2015 Springer International Publishing Switzerland

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Vabishchevich, P.N. (2015). Operator-Difference Scheme with a Factorized Operator. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2015. Lecture Notes in Computer Science(), vol 9374. Springer, Cham. https://doi.org/10.1007/978-3-319-26520-9_7

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  • DOI: https://doi.org/10.1007/978-3-319-26520-9_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26519-3

  • Online ISBN: 978-3-319-26520-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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