01.01.07; 01.02.04 (Computing mathematics; Mechanics of deformable solids)
Birth date:
27.04.1939
E-mail:
Keywords:
integral tranforms; integral transforms' inversion; Laplace transform; Fourier transform; quadrature formulas; ill-posed problems.
Subject:
Convergence for quadrature formulas of highest degree of precision with increasing number of nodes that are used for the numerical Laplace transform inversion and generated delta-like kernels are investigated. Methods of evaluation for the jumps of inverse transform and his derivatives by means of quadrature formulas are proposed. Methods of quadrature formulas' construction for the Laplace transform numerical inversion by using PC are also proposed. Methods of inversion that use the Laguerre functions are developed.
Biography
Graduated from Faculty of Mathematics and Mechanics of St. Petersburg State University (SPSU) in 1961 (department of computational mathematics). Ph.D. thesis was defended in 1975. D.Sci. thesis was defended in 1991. A list of my works contains more than 100 titles.
Main publications:
Ryabov V. M. Priblizhennoe vychislenie preobrazovaniya Fure i ego obrascheniya. Metody vychislenii // Vyp. 18. SPb. 1999. 187–195.
A. V. Lebedeva, V. M. Ryabov, “On the properties of some inversion methods of the Laplace transform”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 10:1 (2023), 36–46; Vestn. St. Petersbg. Univ., Math., 56:1 (2023), 27–34
2018
2.
V. M. Ryabov, I. G. Burova, M. A. Kalnitskaya, A. V. Malevich, A. V. Lebedeva, A. N. Borzykh, “On numerical solution of systems of linear algebraic equations with ill-conditioned matrices”, Meždunar. nauč.-issled. žurn., 2018, no. 12(78), 13–17
2017
3.
A. V. Lebedeva, V. M. Ryabov, “On the construction of quadrature rules for Laplace transform inversion”, Zh. Vychisl. Mat. Mat. Fiz., 57:11 (2017), 1782–1787; Comput. Math. Math. Phys., 57:11 (2017), 1751–1756
2015
4.
A. V. Lebedeva, V. M. Ryabov, “On integration contour deformation in a Laplace transform inversion formula”, Zh. Vychisl. Mat. Mat. Fiz., 55:7 (2015), 1118–1124; Comput. Math. Math. Phys., 55:7 (2015), 1103–1109
A. V. Lebedeva, V. M. Ryabov, “Special quadrature rules for Laplace transform inversion”, Zh. Vychisl. Mat. Mat. Fiz., 52:12 (2012), 2133–2139; Comput. Math. Math. Phys., 52:12 (2012), 1597–1602
2009
6.
M. M. Kabardov, V. M. Ryabov, “Acceleration of the convergence of the Laguerre series in the problem of inverting the Laplace transform”, Zh. Vychisl. Mat. Mat. Fiz., 49:4 (2009), 601–610; Comput. Math. Math. Phys., 49:4 (2009), 579–588
V. M. Ryabov, “On quadratures related to Padé approximants for the inversion of the Laplace transform”, Zh. Vychisl. Mat. Mat. Fiz., 46:5 (2006), 771–780; Comput. Math. Math. Phys., 46:5 (2006), 733–742
2004
8.
V. M. Ryabov, “Jump determination for an original function by using its Laplace transform”, Zh. Vychisl. Mat. Mat. Fiz., 44:5 (2004), 777–785; Comput. Math. Math. Phys., 44:5 (2004), 732–739
1996
9.
V. M. Ryabov, “Quadrature formulae for evaluating singular integrals of oscillating functions”, Zh. Vychisl. Mat. Mat. Fiz., 36:8 (1996), 39–44; Comput. Math. Math. Phys., 36:8 (1996), 1011–1015
V. M. Ryabov, “The properties of quadrature formulas of the highest accuracy used for Laplace transform inversion”, Zh. Vychisl. Mat. Mat. Fiz., 29:7 (1989), 1083–1087; U.S.S.R. Comput. Math. Math. Phys., 29:4 (1989), 83–86
V. M. Ryabov, “The properties of quadrature formulae used for the inversion of Laplace transforms”, Zh. Vychisl. Mat. Mat. Fiz., 29:6 (1989), 941–944; U.S.S.R. Comput. Math. Math. Phys., 29:3 (1989), 207–209
1973
12.
M. K. Gavurin, V. M. Ryabov, “Application of Chebyshev polynomials to the regularization of ill-posed and ill-conditioned equations in Hilbert space”, Zh. Vychisl. Mat. Mat. Fiz., 13:6 (1973), 1599–1601; U.S.S.R. Comput. Math. Math. Phys., 13:6 (1973), 283–287
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