Home page of Malykh M.D.

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Research

• A. N. Bogolyubov, M. D. Malykh, and A. G. Sveshnikov. Instability of eigenvalues embedded in the waveguide's continuous spectrum with respect to perturbations of its filling // Doklady Mathematics. Vol. 66, No. 1, 2002. Pag. 140.
  [pdf]
• M. D. Malykh. On transcendental functions arising from integrating differential equations in finite terms // Journal of Mathematical Sciences: Volume 209, Issue 6 (2015), Page 935-952.
  [pdf] [ref]
• M. D. Malykh. On integration of the first order differential equations in finite terms // Journal of Physics: Conference Series, v. 788, p. 012026
  [pdf]
• M. D. Malykh and L. A. Sevastianov. On an example of a system of differential equations that are integrated in Abelian functions // Journal of Physics, v. 937, p. 012027
  [pdf]
• M. D. Malykh and L. A. Sevastianov. Finite difference schemes as algebraic correspondences between layers // EPJ Web of Conferences, v. 173, p. 0301
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• V. P. Gerdt, M. D. Malykh, L. A. Sevastianov, Yu Ying. On conservative difference schemes for the many-body problem, 2020.
  [arxiv.org] [midpoint.sage v. 0.9]
• M. Malykh, M. Gambaryan, O. Kroytor, and A. Zorin. Finite Difference Models of Dynamical Systems with Quadratic Right-Hand Side // Mathematics 2024, 12, 167.
  [pdf, en]

Sagemath

• [lagutinski.sage] is a small package for solving ODEs or system of ODE in algebraic functions. Description was presented in my report on PCA'2016. Refs.:
  [1.] M. D. Malykh. On M.N. Lagutinski method for integration of ordinary differential equations // Report on PCA'2016, SPb., 20 apr. 2016.
  [pdf]
• [weierstrass.sage] is a small package for the work with abelian integrals. Description was presented in my report on PCA'2017. Refs.:
  [1.] M.D. Malykh, L.A. Sevastianov. Weierstrass Theory of Abelian Integrals and its Realization in Sage // Report on PCA'2017, SPb., 18 apr. 2017.
  [pdf]
• [cros.sage] is a small package for the work with complex Rosenbrock scheme.
  [1.] A. Baddour, M. D. Malykh, A. A. Panin, L. A. Sevastianov, Numerical determination of the singularity order of a system of differential equations // Discrete and Continuous Models and Applied Computational Science 28 (1) (2020) P. 17-34. DOI: 10.22363/2658-4670-2020-28-1-17-34.
• [midpoint.sage v. 0.9] is a small package for the work with midpoint scheme.
  [1.] V. P. Gerdt, M. D. Malykh, L. A. Sevastianov, Yu Ying. On conservative difference schemes for the many-body problem, 2020.
  [arxiv.org]

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