In Memory of Vladimir Gerdt

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Abstract

Center for Computational Methods in Applied Mathematics of RUDN, Professor V.P. Gerdt, whose passing was a great loss to the scientific center and the computer algebra community. The article provides biographical information about V.P. Gerdt, talks about his contribution to the development of computer algebra in Russia and the world. At the end there are the author’s personal memories of V.P. Gerdt.

About the authors

Victor F. Edneral

Lomonosov Moscow State University; Peoples’ Friendship University of Russia (RUDN University)

Author for correspondence.
Email: edneral@theory.sinp.msu.ru
ORCID iD: 0000-0002-5125-0603

Candidate of Physical and Mathematical Sciences, Senior Researcher of Skobeltsyn Institute of Nuclear Physics

1 (2), Leninskie Gory, Moscow, 119991, Russian Federation; 6, Miklukho-Maklaya St., Moscow, 117198, Russian Federation

References

  1. C. Riquier, Les Systèmes d’Equations aux Dérivées Partielles. Paris: Gauthier-Villars, 1910.
  2. M. Janet, “Systèmes d’équations aux dérivées partielles,” Journals de mathématiques, 8e série, vol. 3, pp. 65-151, 1920.
  3. J. Thomas, Differential systems. New York: American Mathematical Society, 1937.
  4. D. Robertz, Formal algorithmic elimination for PDEs. Springer, 2014.
  5. D. Cox, J. Little, and D. O’Shea, Ideals, varieties, and algorithms, 3rd ed. Springer, 2007.
  6. F. S. Macaulay, “Some properties of enumeration in the theory of modular systems,” Proceedings of the London Mathematical Society, vol. s2-26, no. 1, pp. 531-555, 1927. doi: 10.1112/plms/s2-26.1.531.
  7. A. Y. Zharkov and Y. A. Blinkov, “Involution approach to solving systems of algebraic equations,” in Proceedings of the 1993 International IMACS Symposium on Symbolic Computation. Laboratoire d’Informatique Fondamentale de Lille, France, 1993, pp. 11-16.
  8. A. Y. Zharkov, “Involutive polynomial bases: General case,” in Preprint JINR E5-94-224. Dubna, 1994.
  9. A. Y. Zharkov and Y. A. Blinkov, “Algorithm for constructing involutive bases of polynomial ideal,” in International Conference on Interval and Computer-Algebraic Methods in Science and Engineering. St-Petersburg, 1994, pp. 258-260.
  10. A. Y. Zharkov and Y. A. Blinkov, “Involutive bases of zero-dimensional ideals,” in Preprint JINR E5-94-318. Dubna, 1994.
  11. V. P. Gerdt, “Gröbner bases and involutive methods for algebraic and differential equations,” in Computer Algebra in Science and Engineering. Singapore: World Scientific, 1995, pp. 117-137.
  12. J. Apel, “A Gröbner approach to involutive bases,” Journal of Symbolic Computation, vol. 19, no. 5, pp. 441-458, 1995.
  13. V. P. Gerdt and Y. A. Blinkov, “Involutive polynomial bases,” in Publication IT-95-271. Laboratoire d’Informatique Fondamentale de Lille, 1995.
  14. V. P. Gerdt and Y. A. Blinkov, “Involutive Bases of Polynomial Ideals,” in Preprint-Nr.1/1996. Naturwissenschaftlich-Theoretisches Zentrum, University of Leipzig, 1996.
  15. V. P. Gerdt, “Gröbner bases and involutive methods for algebraic and differential equations,” Mathematical and computer modelling, vol. 25, no. 8-9, pp. 75-90, 1997. doi: 10.1016/S0895-7177(97)00060-5.
  16. V. P. Gerdt and Y. A. Blinkov, “Involutive bases of polynomial ideals,” in Preprint JINR E5-97-3. Dubna, 1997.
  17. V. P. Gerdt, “Involutive divisions in mathematica: Implementation and some applications,” in Proceedings of the Rhein Workshop on Computer Algebra. Institute for Algorithms and Scientific Computing, GMD-SCAI, 1998, pp. 74-91.
  18. V. P. Gerdt and Y. A. Blinkov, “Involutive divisions of monomials,” Programming and Computer Software, vol. 24, no. 6, pp. 283-285, 1998.
  19. Y. A. Blinkov, “Division and algorithms in the ideal membership problem [Deleniye i algoritmy v zadache o prinadlezhnosti k idealu],” Izvestija Saratovskogo universiteta, vol. 1, no. 2, pp. 156-167, 2001, In Russian.
  20. K. Lipnikov, G. Manzini, and M. Shashkov, “Mimetic finite difference method,” Journal of Computational Physics, vol. 257, pp. 1163-1227, 2014. doi: 10.1016/j.jcp.2013.07.031.
  21. B. Koren, R. Abgrall, P. Bochev, J. Frank, and B. Perot, “Physicscompatible numerical methods,” Journal of Computational Physics, vol. 257, no. Part B, pp. 1039-1524, 2014. doi: 10.1016/j.jcp.2013.10.015.
  22. M. Shashkov, Conservative finite difference methods. Boca Raton: CRC Press, 1996.
  23. D. Arnold, P. Bonchev, R. Lehoucq, R. Nikolaides, and M. Shashkov, Compatible spatial discretizations. Springer-Verlag, Berlin, 2006.
  24. L. B. da Veiga, K. Lipnikov, and G. Manzini, The mimetic finite difference method for elliptic problems. Springer, 2014, vol. 11.
  25. J. E. Castillo and G. F. Miranda, Mimetic discretization methods. Chapman and Hall/CRC, 2013.
  26. V. P. Gerdt, D. Robertz, and Y. A. Blinkov, “Strong Consistency and Thomas Decomposition of Finite Difference Approximations to Systems of Partial Differential Equations,” 2020. arXiv: 2009.01731[cs.SC].

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