Edit Profile (opens in new tab) Gavrilyuk, Ivan P. Co-Author Distance Author ID: gavrilyuk.ivan-p Published as: Gavrilyuk, I. P.; Gavrilyuk, Ivan P.; Gavrilyuk, Ivan; Gavrylyuk, I. P.; Gavrilyuk, I.; Gawrilyuk, I. P.; Gavrilyuk, Ī. P.; Gavrylyuk, I.; Gawriljuk, I. more...less External Links: MGP · ORCID · Google Scholar · dblp Documents Indexed: 163 Publications since 1971, including 4 Books and 1 Additional arXiv Preprint 2 Contributions as Editor Reviewing Activity: 88 Reviews Co-Authors: 60 Co-Authors with 142 Joint Publications 968 Co-Co-Authors all top 5 Co-Authors 23 single-authored 93 Makarov, Volodymyr Leonidovych 14 Timokha, Alexander N. 13 Hermann, Martin 11 Bondarenko, L. N. 11 Zhuk, P. F. 10 Vojtsekhovskyj, S. A. 9 Khoromskiĭ, Boris Nikolaevich 8 Lukovsky, Ivan Oleksandrovych 8 Vasylyk, Vitaliĭ Borysovych 7 Kutniv, Myroslav V. 7 Luzhnykh, V. M. 5 Hackbusch, Wolfgang 5 Sazhenyuk, Volodymyr S. 5 Trotsenko, Yuriy 4 Lazurchak, I. I. 4 Pirnazarov, S. P. 4 Rossokhataya, N. A. 3 Bandyrskii, B. I. 3 Grekov, L. D. 3 Trotsenko, Volodymyr 2 Arov, Damir Zyamovich 2 Kulyk, Anatoli B. 2 Lazarov, Raytcho D. 2 Makarov, L. V. 2 Mayko, Nataliya Valentynivna 2 Romanyuk, Nataliia Mykolaivna 2 Rossokhata, Nataliya O. 2 Rossokhatyĭ, V. K. 2 Samarskiĭ, Aleksandr Andreevich 2 Shmanenko, T. L. 2 Solodun, O. V. 2 Sytnyk, D. O. 1 Barnyak, Mykhalio 1 Beyer, Klaus 1 Bohonova, T. Ju. 1 Bohonova, T. Yu. 1 Burkivs’ka, V. L. 1 Chalenko, P. I. 1 Chapko, Roman 1 Demkiv, Ihor 1 Elenin, G. G. 1 Günther, Matthias 1 Khimich, A. N. 1 Klimenko, Alexey V. 1 Klymenko, A. V. 1 Kopistira, M. P. 1 Kravez, I. S. 1 Kulik, A. B. 1 Makarov, I. L. 1 Moskal’kov, M. N. 1 Moskal’kov, Mykhajlo M. 1 Prikazchikov, Viktor G. 1 Rossokhataya, Nataliya 1 Rossokhaty, Victor 1 Ryabichev, Vyacheslav L. 1 Shan’ko, T. M. 1 Tyrtyshnikov, Evgeniĭ Evgen’evich 1 Vejtsekhovskij, S. A. 1 Zdorenko, Yu. N. 1 Zmitrenko, Nikolaĭ Vasil’evich all top 5 Serials 22 Vychislitel’naya i Prikladnaya Matematika 21 Computational Methods in Applied Mathematics 9 Journal of Soviet Mathematics 7 Numerical Functional Analysis and Optimization 6 Ukrainian Mathematical Journal 6 Dopovidi Natsional’noï Akademiï Nauk Ukraïny. Matematyka, Pryrodoznavstvo, Tekhnichni Nauky 5 Differential Equations 4 Doklady Akademii Nauk Ukrainskoĭ SSR, Seriya A 4 Journal of Engineering Mathematics 4 Mathematics of Computation 4 Soviet Mathematics 4 Journal of Mathematical Sciences (New York) 3 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 3 SIAM Journal on Numerical Analysis 3 Zeitschrift für Analysis und ihre Anwendungen 3 U.S.S.R. Computational Mathematics and Mathematical Physics 3 Visnyk. Seriya: Fizyko-Matematychni Nauky. Kyïvs’kyĭ Universytet Imeni Tarasa Shevchenka 2 Izvestiya Vysshikh Uchebnykh Zavedeniĭ, Matematika 2 Ukraïns’kyĭ Matematychnyĭ Zhurnal 2 Fluid Dynamics Research 2 Differentsial’nye Uravneniya 2 Journal of Integral Equations and Applications 2 Dopovidi Akademiï Nauk Ukraïns’koï RSR. Seriya A 2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 2 Zhurnal Obchyslyuval’noïta Prykladnoï Matematyky 2 Applied Mathematics and Informatics 2 Matematicheskoe Modelirovanie 1 IMA Journal of Numerical Analysis 1 International Journal of Solids and Structures 1 Journal of Mathematical Analysis and Applications 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 1 Soviet Applied Mechanics 1 Computing 1 Numerische Mathematik 1 Soviet Mathematics. Doklady 1 Cybernetics 1 Applied Numerical Mathematics 1 Numerical Methods for Partial Differential Equations 1 Applied Mathematics Letters 1 Linear Algebra and its Applications 1 SIAM Journal on Applied Mathematics 1 East-West Journal of Numerical Mathematics 1 Doklady Mathematics 1 Visnyk Kyïvs’kogo Universytetu. Matematyka i Mekhanika 1 Engineering Computations 1 Advances in Difference Equations 1 ISNM. International Series of Numerical Mathematics 1 Zbirnyk Prats’ Instytutu Matematyky NAN Ukraïny 1 Frontiers in Mathematics all top 5 Fields 129 Numerical analysis (65-XX) 65 Partial differential equations (35-XX) 60 Ordinary differential equations (34-XX) 22 Operator theory (47-XX) 15 Fluid mechanics (76-XX) 13 Calculus of variations and optimal control; optimization (49-XX) 10 Integral equations (45-XX) 7 Classical thermodynamics, heat transfer (80-XX) 5 Potential theory (31-XX) 5 Mechanics of deformable solids (74-XX) 5 Optics, electromagnetic theory (78-XX) 3 Special functions (33-XX) 3 Functional analysis (46-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 General and overarching topics; collections (00-XX) 2 Difference and functional equations (39-XX) 2 Approximations and expansions (41-XX) 2 Computer science (68-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Real functions (26-XX) 1 Probability theory and stochastic processes (60-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 78 Publications have been cited 493 times in 256 Documents Cited by ▼ Year ▼ Hierarchical tensor-product approximation to the inverse and related operators for high-dimensional elliptic problems. Zbl 1071.65032 Gavrilyuk, Ivan P.; Hackbusch, Wolfgang; Khoromskij, Boris N. 49 2005 Data-sparse approximation to a class of operator-valued functions. Zbl 1066.65060 Gavrilyuk, Ivan P.; Hackbusch, Wolfgang; Khoromskij, Boris N. 31 2005 Data-sparse approximation to the operator-valued functions of elliptic operator. Zbl 1065.47009 Gavrilyuk, Ivan P.; Hackbusch, Wolfgang; Khoromskij, Boris N. 30 2004 \(\mathcal H\)-matrix approximation for the operator exponential with applications. Zbl 1005.65113 Gavrilyuk, Ivan P.; Hackbusch, Wolfgang; Khoromskij, Boris N. 28 2002 Exponentially convergent algorithms for the operator exponential with applications to inhomogeneous problems in Banach spaces. Zbl 1116.65063 Gavrilyuk, I. P.; Makarov, V. L. 23 2005 Exponentially convergent parallel discretization methods for the first order evolution equations. Zbl 0998.65056 Gavrilyuk, I.; Makarov, V. 18 2001 Representation and approximation of the solution of an initial value problem for a first order differential equation in Banach spaces. Zbl 0849.65040 Gavrilyuk, I. P.; Makarov, V. L. 15 1996 Sloshing in a vertical circular cylindrical tank with an annular baffle. I: Linear fundamental solutions. Zbl 1101.76008 Gavrilyuk, I.; Lukovsky, I.; Trotsenko, Yu.; Timokha, A. 12 2006 A method for solving initial value problems for linear differential equations in Hilbert space based on the Cayley transform. Zbl 0798.34064 Arov, Damir Z.; Gavrilyuk, Ivan P. 12 1993 Sloshing in a vertical circular cylindrical tank with an annular baffle. II: Nonlinear resonant waves. Zbl 1107.76012 Gavrilyuk, I.; Lukovsky, I.; Trotsenko, Yu.; Timokha, A. 11 2007 Exact and truncated difference schemes for boundary value ODEs. Zbl 1226.65066 Gavrilyuk, Ivan P.; Hermann, Martin; Makarov, Volodymyr L.; Kutniv, Myroslav V. 11 2011 Strongly \(P\)-positive operators and explicit representations of the solutions of initial value problems for second-order differential equations in Banach space. Zbl 0944.34050 Gavrilyuk, Ivan P. 11 1999 Stability and regularization of three-level difference schemes with unbounded operator coefficients in Banach spaces. Zbl 1002.65101 Samarskii, Alexander A.; Gavrilyuk, Ivan P.; Makarov, Vladimir L. 11 2001 The Cayley transform and the solution of an initial value problem for a first order differential equation with an unbounded operator coefficient in Hilbert space. Zbl 0802.47049 Gavrilyuk, Ivan P.; Makarov, Vladimir L. 11 1994 Linear and nonlinear sloshing in a circular conical tank. Zbl 1153.76328 Gavrilyuk, I. P.; Lukovsky, I. A.; Timokha, A. N. 9 2005 Exponentially convergent algorithms for abstract differential equations. Zbl 1225.47001 Gavrilyuk, Ivan; Makarov, Volodymyr; Vasylyk, Vitalii 9 2011 An algorithmic representation of fractional powers of positive operators. Zbl 0860.47011 Gavrilyuk, Ivan P. 9 1996 Representation and approximation of solutions of initial value problems for differential equations in Hilbert space based on the Cayley transform. Zbl 0828.34045 Arov, D. Z.; Gavrilyuk, I. P.; Makarov, V. L. 8 1995 Quantized-TT-Cayley transform for computing the dynamics and the spectrum of high-dimensional Hamiltonians. Zbl 1283.65036 Gavrilyuk, Ivan; Khoromskij, Boris 8 2011 Super-exponentially convergent parallel algorithm for a fractional eigenvalue problem of Jacobi-type. Zbl 1382.65216 Gavrilyuk, Ivan; Makarov, Volodymyr; Romaniuk, Nataliia 7 2018 Explicit and approximate solutions of second-order evolution differential equations in Hilbert space. Zbl 0939.65084 Gavrilyuk, Ivan P.; Makarov, Vladimir L. 7 1999 Two-dimensional variational vibroequilibria and Faraday’s drops. Zbl 1125.76372 Gavrilyuk, Ivan; Lukovsky, Ivan; Timokha, Alexander 7 2004 Strongly positive operators and numerical algorithms without accuracy saturation. (Сильно позитивные операторы и численные алгоритмы без насыщения точности.) Zbl 1150.65300 Gavrilyuk, I. P.; Makarov, V. L. 6 2004 \(\mathcal H\)-matrix approximation for elliptic solution operators in cylinder domains. Zbl 1012.65134 Gavrilyuk, I. P.; Hackbusch, W.; Khoromskij, B. N. 6 2001 Exponentially convergent parallel algorithm for nonlinear eigenvalue problems. Zbl 1130.65078 Gavrilyuk, I. P.; Klimenko, A. V.; Makarov, V. L.; Rossokhata, N. O. 6 2007 Super-exponentially convergent parallel algorithm for eigenvalue problems with fractional derivatives. Zbl 1352.65201 Demkiv, Ihor; Gavrilyuk, Ivan P.; Makarov, Volodymyr L. 6 2016 Super exponentially convergent approximation to the solution of the Schrödinger equation in abstract setting. Zbl 1283.65046 Gavrilyuk, I. P. 6 2010 Functional-discrete method (FD-method) for matrix Sturm-Liouville problems. Zbl 1088.65074 Bandyrskii, B. Ĭ.; Gavrilyuk, I. P.; Lazurchak, I. I.; Makarov, V. L. 5 2005 Exponentially convergent parallel discretization method for the first order evolution equation. Zbl 1066.65063 Makarov, V. L.; Gavrilyuk, I. P. 5 2000 Natural sloshing frequencies in rigid truncated conical tanks. Zbl 1257.76002 Gavrilyuk, I.; Hermann, M.; Lukovsky, I.; Solodun, O.; Timokha, A. 5 2008 Difference schemes for nonlinear BVPs using Runge-Kutta IVP-solvers. Zbl 1139.65057 Gavrilyuk, I. P.; Hermann, M.; Kutniv, M. V.; Makarov, V. L. 4 2006 Estimates of the rate of convergence of difference schemes for fourth- order elliptic equations. Zbl 0541.65064 Gavrilyuk, I. P.; Lazarov, R. D.; Makarov, V. L.; Pirnazarov, S. P. 4 1983 Analytical velocity potentials in cells with a rigid spherical wall. Zbl 1380.76008 Barnyak, Mykhalio; Gavrilyuk, Ivan; Hermann, Martin; Timokha, Alexander 4 2011 Exact and approximate solutions of some operator equations based on the Cayley transform. Zbl 0938.47013 Gavrilyuk, Ivan P.; Makarov, Vladimir L. 4 1998 Explicit and approximate solutions of second order elliptic differential equations in Hilbert and Banach spaces. Zbl 0939.65085 Gavrilyuk, Ivan P.; Makarov, Vladimir L. 4 1999 Adaptive algorithms based on exact difference schemes for nonlinear BVPs on the half-axis. Zbl 1162.65371 Gavrilyuk, I. P.; Hermann, M.; Kutniv, M. V.; Makarov, V. L. 4 2009 Compressible potential flows with free boundaries. I: Vibrocapillary equilibria. Zbl 1005.35076 Beyer, K.; Gawriljuk, I.; Günther, M.; Lukovsky, I.; Timokha, A. 4 2001 On the numerical solution of linear evolution problems with an integral operator coefficient. Zbl 0974.65057 Gavrilyuk, I.; Makarov, V.; Chapko, R. 4 1999 Algorithms without accuracy saturation for evolution equations in Hilbert and Banach spaces. Zbl 1066.65061 Gavrilyuk, Ivan P.; Makarov, Volodymyr L. 4 2005 A two-point difference scheme of an arbitrary order of accuracy for BVPs for systems of first order nonlinear ODEs. Zbl 1068.65102 Makarov, V. L.; Gavrilyuk, I. P.; Kutniv, M. V.; Hermann, M. 4 2004 Ein exaktes Differenzenschema und abgeschnittene Differenzenschemata für eine gewisse Klasse Sturm-Liouvillescher Probleme mit Entartung. Zbl 0438.65071 Makarov, V. L.; Gavrilyuk, I. P.; Luzhnykh, V. M. 4 1980 Resonant equations with classical orthogonal polynomials. I. Zbl 1437.34043 Gavrilyuk, I.; Makarov, V. 4 2019 Weakly nonlinear sloshing in a truncated circular conical tank. Zbl 1431.76028 Gavrilyuk, I. P.; Hermann, M.; Lukovsky, I. A.; Solodun, O. V.; Timokha, A. N. 4 2013 Difference schemes for nonlinear BVPs on the semiaxis. Zbl 1149.65061 Gavrilyuk, I. P.; Hermann, M.; Kutniv, M. V.; Makarov, V. L. 3 2007 Evolutional problems of the contained fluid. With a foreword by Martin Hermann. Zbl 1150.76001 Gavrilyuk, Ivan P.; Lukovsky, Ivan A.; Makarov, Vladimir L.; Timokha, Alexander N. 3 2006 Integral equations of the linear sloshing in an infinite chute and their discretization. Zbl 1029.76004 Gavrilyuk, Ivan P.; Kulyk, Anatoli B.; Makarov, Vladimir L. 3 2001 A method with a controllable exponential convergence rate for nonlinear differential operator equations. Zbl 1170.65039 Gavrilyuk, I. P.; Makarov, V. L.; Lazurchak, I. I.; Sytnyk, D. 3 2009 Quasi-optimal rank-structured approximation to multidimensional parabolic problems by Cayley transform and Chebyshev interpolation. Zbl 1420.65056 Gavrilyuk, Ivan; Khoromskij, Boris N. 3 2019 Exponentially convergent method for the \(m\)-point nonlocal problem for a first order differential equation in Banach space. Zbl 1193.65080 Gavrilyuk, I. P.; Makarov, V. L.; Sytnyk, D. O.; Vasylyk, V. B. 3 2010 Eigenoscillations of three- and two-element flexible systems. Zbl 1194.74136 Gavrilyuk, I.; Hermann, M.; Trotsenko, Yu.; Timokha, A. 3 2010 Resonant equations with classical orthogonal polynomials. II. Zbl 1441.34049 Gavrilyuk, I.; Makarov, V. 3 2019 Compatible estimates for the rate of convergence of difference solutions to generalized solutions of the first boundary value problem for fourth order equations. Zbl 0541.65062 Gavrilyuk, I. P.; Makarov, V. L.; Pirnazarov, S. P. 2 1983 Axisymmetric oscillations of a cupola-shaped shell. Zbl 1310.74026 Gavrilyuk, Ivan; Hermann, Martin; Trotsenko, Volodymyr; Trotsenko, Yuriy; Timokha, Alexander 2 2010 Some new discretizations of evolution equations. Zbl 0968.65032 Gavrilyuk, I. P. 2 1999 Exponentially convergent approximation to the elliptic solution operator. Zbl 1117.65078 Gavrilyuk, I. P.; Makarov, V. L.; Vasylyk, V. 2 2006 Exact difference schemes and difference schemes of arbitrary given degree of accuracy for generalized one-dimensional third boundary value problems. Zbl 0779.65047 Gawrilyuk, I. P. 2 1993 Approximation of the operator exponential and applications. Zbl 1143.34035 Gavrilyuk, I. P. 2 2007 Weighted estimates for boundary value problems with fractional derivatives. Zbl 1451.65171 Gavrilyuk, Ivan P.; Makarov, Volodymyr L.; Mayko, Nataliya V. 2 2020 Exponentially convergent method for an abstract integro-differential equation with fractional Hardy-Titchmarsh integral. Zbl 1474.65501 Makarov, V. L.; Gavrylyuk, I. P.; Vasylyk, V. B. 2 2021 An exponentially convergent algorithm for nonlinear differential equations in Banach spaces. Zbl 1126.65118 Gavrilyuk, Ivan P.; Makarov, Volodymyr L. 1 2007 A class of fully discrete approximations for the first order differential equations in Banach spaces with uniform estimates on the whole of \(\mathbb{R}^+\). Zbl 0961.65052 Gavrilyuk, Ivan P. 1 1999 Consistent estimates for the speed of convergence of difference solutions to generalized solutions of the first boundary-value problem for fourth order equations. Zbl 0566.65071 Gavrilyuk, I. P.; Makarov, V. L.; Pirnazarov, S. P. 1 1983 An explicit boundary integral representation of the solution of the two-dimensional heat equation and its discretization. Zbl 0980.65099 Gavrilyuk, I. P.; Makarov, V. L. 1 2000 Exponentially convergent methods of parallel discretization for the first order evolution equations. Zbl 0995.65104 Makarov, V. L.; Gavrylyuk, I. P. 1 2002 Economic method for solving boundary value problems for a class of quasilinear equations containing the Laplace operator. Zbl 0474.35009 Gavrilyuk, I. P. 1 1980 A parallel method of high accuracy for the first order evolution equation in Hilbert and Banach spaces. Zbl 1047.65034 Gavrilyuk, Ivan P.; Makarov, Vladimir L.; Ryabichev, Vyacheslav L. 1 2003 A Nysróm-Kress scheme for a Dirichlet-Neumann boundary value problem associated with fluid sloshing in a rectangular tank. Zbl 1097.76577 Gavrilyuk, I. P.; Timokha, A. N. 1 2003 Exponentially convergent Duhamel-like algorithms for differential equations with an operator coefficient possessing a variable domain in a Banach space. Zbl 1160.65020 Bohonova, T. Yu.; Gavrilyuk, I. P.; Makarov, V. L.; Vasylyk, V. 1 2008 An exact and truncated difference schemes for boundary value problems with degeneration. Zbl 0579.65076 Gavrilyuk, I. P.; Luzhnykh, V. M.; Makarov, V. L. 1 1985 Convergence of finite-difference solutions to generalized solutions of the first boundary-value problem for a fourth-order quasilinear equation in regions of arbitrary shape. Zbl 0601.65072 Vojtsekhovskij, S. A.; Gavrilyuk, I. P. 1 1985 A new estimate of the sinc method for linear parabolic problems including the initial point. Zbl 1069.65100 Gavrilyuk, Ivan P.; Makarov, Vladimir L.; Vasylyk, Vitaliy 1 2004 Algorithms without accuracy saturation and exponential convergent algorithms for operator equations. Zbl 1064.65514 Gavrilyuk, Ivan P. 1 2003 Difference schemes for a fourth order one-dimensional equation with the nonlinear boundary condition. Zbl 0711.65061 Gavrilyuk, I. P.; Grekov, L. D. 1 1989 Exact and truncated difference schemes for boundary-value problem. Zbl 1362.65077 Gavrilyuk, Ivan; Kutniv, Myroslav; Makarov, Volodymyr 1 2016 Eigenoscillations of a thin-walled azimuthally closed, axially open shell of revolution. Zbl 1359.74135 Gavrilyuk, I.; Hermann, M.; Trotsenko, V.; Trotsenko, Yu.; Timokha, A. 1 2014 Superexponentially convergent algorithm for an abstract eigenvalue problem with applications to ordinary differential equations. Zbl 1361.65033 Gavrilyuk, I. P.; Makarov, V. L.; Romanyuk, N. M. 1 2017 Editorial. Tensor numerical methods: actual theory and recent applications. Zbl 1422.00020 1 2019 Resonant equations and classical orthogonal polynomials. Zbl 1424.47115 Gavrylyuk, I. P.; Makarov, V. L. 1 2018 Exponentially convergent method for an abstract integro-differential equation with fractional Hardy-Titchmarsh integral. Zbl 1474.65501 Makarov, V. L.; Gavrylyuk, I. P.; Vasylyk, V. B. 2 2021 Weighted estimates for boundary value problems with fractional derivatives. Zbl 1451.65171 Gavrilyuk, Ivan P.; Makarov, Volodymyr L.; Mayko, Nataliya V. 2 2020 Resonant equations with classical orthogonal polynomials. I. Zbl 1437.34043 Gavrilyuk, I.; Makarov, V. 4 2019 Quasi-optimal rank-structured approximation to multidimensional parabolic problems by Cayley transform and Chebyshev interpolation. Zbl 1420.65056 Gavrilyuk, Ivan; Khoromskij, Boris N. 3 2019 Resonant equations with classical orthogonal polynomials. II. Zbl 1441.34049 Gavrilyuk, I.; Makarov, V. 3 2019 Editorial. Tensor numerical methods: actual theory and recent applications. Zbl 1422.00020 1 2019 Super-exponentially convergent parallel algorithm for a fractional eigenvalue problem of Jacobi-type. Zbl 1382.65216 Gavrilyuk, Ivan; Makarov, Volodymyr; Romaniuk, Nataliia 7 2018 Resonant equations and classical orthogonal polynomials. Zbl 1424.47115 Gavrylyuk, I. P.; Makarov, V. L. 1 2018 Superexponentially convergent algorithm for an abstract eigenvalue problem with applications to ordinary differential equations. Zbl 1361.65033 Gavrilyuk, I. P.; Makarov, V. L.; Romanyuk, N. M. 1 2017 Super-exponentially convergent parallel algorithm for eigenvalue problems with fractional derivatives. Zbl 1352.65201 Demkiv, Ihor; Gavrilyuk, Ivan P.; Makarov, Volodymyr L. 6 2016 Exact and truncated difference schemes for boundary-value problem. Zbl 1362.65077 Gavrilyuk, Ivan; Kutniv, Myroslav; Makarov, Volodymyr 1 2016 Eigenoscillations of a thin-walled azimuthally closed, axially open shell of revolution. Zbl 1359.74135 Gavrilyuk, I.; Hermann, M.; Trotsenko, V.; Trotsenko, Yu.; Timokha, A. 1 2014 Weakly nonlinear sloshing in a truncated circular conical tank. Zbl 1431.76028 Gavrilyuk, I. P.; Hermann, M.; Lukovsky, I. A.; Solodun, O. V.; Timokha, A. N. 4 2013 Exact and truncated difference schemes for boundary value ODEs. Zbl 1226.65066 Gavrilyuk, Ivan P.; Hermann, Martin; Makarov, Volodymyr L.; Kutniv, Myroslav V. 11 2011 Exponentially convergent algorithms for abstract differential equations. Zbl 1225.47001 Gavrilyuk, Ivan; Makarov, Volodymyr; Vasylyk, Vitalii 9 2011 Quantized-TT-Cayley transform for computing the dynamics and the spectrum of high-dimensional Hamiltonians. Zbl 1283.65036 Gavrilyuk, Ivan; Khoromskij, Boris 8 2011 Analytical velocity potentials in cells with a rigid spherical wall. Zbl 1380.76008 Barnyak, Mykhalio; Gavrilyuk, Ivan; Hermann, Martin; Timokha, Alexander 4 2011 Super exponentially convergent approximation to the solution of the Schrödinger equation in abstract setting. Zbl 1283.65046 Gavrilyuk, I. P. 6 2010 Exponentially convergent method for the \(m\)-point nonlocal problem for a first order differential equation in Banach space. Zbl 1193.65080 Gavrilyuk, I. P.; Makarov, V. L.; Sytnyk, D. O.; Vasylyk, V. B. 3 2010 Eigenoscillations of three- and two-element flexible systems. Zbl 1194.74136 Gavrilyuk, I.; Hermann, M.; Trotsenko, Yu.; Timokha, A. 3 2010 Axisymmetric oscillations of a cupola-shaped shell. Zbl 1310.74026 Gavrilyuk, Ivan; Hermann, Martin; Trotsenko, Volodymyr; Trotsenko, Yuriy; Timokha, Alexander 2 2010 Adaptive algorithms based on exact difference schemes for nonlinear BVPs on the half-axis. Zbl 1162.65371 Gavrilyuk, I. P.; Hermann, M.; Kutniv, M. V.; Makarov, V. L. 4 2009 A method with a controllable exponential convergence rate for nonlinear differential operator equations. Zbl 1170.65039 Gavrilyuk, I. P.; Makarov, V. L.; Lazurchak, I. I.; Sytnyk, D. 3 2009 Natural sloshing frequencies in rigid truncated conical tanks. Zbl 1257.76002 Gavrilyuk, I.; Hermann, M.; Lukovsky, I.; Solodun, O.; Timokha, A. 5 2008 Exponentially convergent Duhamel-like algorithms for differential equations with an operator coefficient possessing a variable domain in a Banach space. Zbl 1160.65020 Bohonova, T. Yu.; Gavrilyuk, I. P.; Makarov, V. L.; Vasylyk, V. 1 2008 Sloshing in a vertical circular cylindrical tank with an annular baffle. II: Nonlinear resonant waves. Zbl 1107.76012 Gavrilyuk, I.; Lukovsky, I.; Trotsenko, Yu.; Timokha, A. 11 2007 Exponentially convergent parallel algorithm for nonlinear eigenvalue problems. Zbl 1130.65078 Gavrilyuk, I. P.; Klimenko, A. V.; Makarov, V. L.; Rossokhata, N. O. 6 2007 Difference schemes for nonlinear BVPs on the semiaxis. Zbl 1149.65061 Gavrilyuk, I. P.; Hermann, M.; Kutniv, M. V.; Makarov, V. L. 3 2007 Approximation of the operator exponential and applications. Zbl 1143.34035 Gavrilyuk, I. P. 2 2007 An exponentially convergent algorithm for nonlinear differential equations in Banach spaces. Zbl 1126.65118 Gavrilyuk, Ivan P.; Makarov, Volodymyr L. 1 2007 Sloshing in a vertical circular cylindrical tank with an annular baffle. I: Linear fundamental solutions. Zbl 1101.76008 Gavrilyuk, I.; Lukovsky, I.; Trotsenko, Yu.; Timokha, A. 12 2006 Difference schemes for nonlinear BVPs using Runge-Kutta IVP-solvers. Zbl 1139.65057 Gavrilyuk, I. P.; Hermann, M.; Kutniv, M. V.; Makarov, V. L. 4 2006 Evolutional problems of the contained fluid. With a foreword by Martin Hermann. Zbl 1150.76001 Gavrilyuk, Ivan P.; Lukovsky, Ivan A.; Makarov, Vladimir L.; Timokha, Alexander N. 3 2006 Exponentially convergent approximation to the elliptic solution operator. Zbl 1117.65078 Gavrilyuk, I. P.; Makarov, V. L.; Vasylyk, V. 2 2006 Hierarchical tensor-product approximation to the inverse and related operators for high-dimensional elliptic problems. Zbl 1071.65032 Gavrilyuk, Ivan P.; Hackbusch, Wolfgang; Khoromskij, Boris N. 49 2005 Data-sparse approximation to a class of operator-valued functions. Zbl 1066.65060 Gavrilyuk, Ivan P.; Hackbusch, Wolfgang; Khoromskij, Boris N. 31 2005 Exponentially convergent algorithms for the operator exponential with applications to inhomogeneous problems in Banach spaces. Zbl 1116.65063 Gavrilyuk, I. P.; Makarov, V. L. 23 2005 Linear and nonlinear sloshing in a circular conical tank. Zbl 1153.76328 Gavrilyuk, I. P.; Lukovsky, I. A.; Timokha, A. N. 9 2005 Functional-discrete method (FD-method) for matrix Sturm-Liouville problems. Zbl 1088.65074 Bandyrskii, B. Ĭ.; Gavrilyuk, I. P.; Lazurchak, I. I.; Makarov, V. L. 5 2005 Algorithms without accuracy saturation for evolution equations in Hilbert and Banach spaces. Zbl 1066.65061 Gavrilyuk, Ivan P.; Makarov, Volodymyr L. 4 2005 Data-sparse approximation to the operator-valued functions of elliptic operator. Zbl 1065.47009 Gavrilyuk, Ivan P.; Hackbusch, Wolfgang; Khoromskij, Boris N. 30 2004 Two-dimensional variational vibroequilibria and Faraday’s drops. Zbl 1125.76372 Gavrilyuk, Ivan; Lukovsky, Ivan; Timokha, Alexander 7 2004 Strongly positive operators and numerical algorithms without accuracy saturation. (Сильно позитивные операторы и численные алгоритмы без насыщения точности.) Zbl 1150.65300 Gavrilyuk, I. P.; Makarov, V. L. 6 2004 A two-point difference scheme of an arbitrary order of accuracy for BVPs for systems of first order nonlinear ODEs. Zbl 1068.65102 Makarov, V. L.; Gavrilyuk, I. P.; Kutniv, M. V.; Hermann, M. 4 2004 A new estimate of the sinc method for linear parabolic problems including the initial point. Zbl 1069.65100 Gavrilyuk, Ivan P.; Makarov, Vladimir L.; Vasylyk, Vitaliy 1 2004 A parallel method of high accuracy for the first order evolution equation in Hilbert and Banach spaces. Zbl 1047.65034 Gavrilyuk, Ivan P.; Makarov, Vladimir L.; Ryabichev, Vyacheslav L. 1 2003 A Nysróm-Kress scheme for a Dirichlet-Neumann boundary value problem associated with fluid sloshing in a rectangular tank. Zbl 1097.76577 Gavrilyuk, I. P.; Timokha, A. N. 1 2003 Algorithms without accuracy saturation and exponential convergent algorithms for operator equations. Zbl 1064.65514 Gavrilyuk, Ivan P. 1 2003 \(\mathcal H\)-matrix approximation for the operator exponential with applications. Zbl 1005.65113 Gavrilyuk, Ivan P.; Hackbusch, Wolfgang; Khoromskij, Boris N. 28 2002 Exponentially convergent methods of parallel discretization for the first order evolution equations. Zbl 0995.65104 Makarov, V. L.; Gavrylyuk, I. P. 1 2002 Exponentially convergent parallel discretization methods for the first order evolution equations. Zbl 0998.65056 Gavrilyuk, I.; Makarov, V. 18 2001 Stability and regularization of three-level difference schemes with unbounded operator coefficients in Banach spaces. Zbl 1002.65101 Samarskii, Alexander A.; Gavrilyuk, Ivan P.; Makarov, Vladimir L. 11 2001 \(\mathcal H\)-matrix approximation for elliptic solution operators in cylinder domains. Zbl 1012.65134 Gavrilyuk, I. P.; Hackbusch, W.; Khoromskij, B. N. 6 2001 Compressible potential flows with free boundaries. I: Vibrocapillary equilibria. Zbl 1005.35076 Beyer, K.; Gawriljuk, I.; Günther, M.; Lukovsky, I.; Timokha, A. 4 2001 Integral equations of the linear sloshing in an infinite chute and their discretization. Zbl 1029.76004 Gavrilyuk, Ivan P.; Kulyk, Anatoli B.; Makarov, Vladimir L. 3 2001 Exponentially convergent parallel discretization method for the first order evolution equation. Zbl 1066.65063 Makarov, V. L.; Gavrilyuk, I. P. 5 2000 An explicit boundary integral representation of the solution of the two-dimensional heat equation and its discretization. Zbl 0980.65099 Gavrilyuk, I. P.; Makarov, V. L. 1 2000 Strongly \(P\)-positive operators and explicit representations of the solutions of initial value problems for second-order differential equations in Banach space. Zbl 0944.34050 Gavrilyuk, Ivan P. 11 1999 Explicit and approximate solutions of second-order evolution differential equations in Hilbert space. Zbl 0939.65084 Gavrilyuk, Ivan P.; Makarov, Vladimir L. 7 1999 Explicit and approximate solutions of second order elliptic differential equations in Hilbert and Banach spaces. Zbl 0939.65085 Gavrilyuk, Ivan P.; Makarov, Vladimir L. 4 1999 On the numerical solution of linear evolution problems with an integral operator coefficient. Zbl 0974.65057 Gavrilyuk, I.; Makarov, V.; Chapko, R. 4 1999 Some new discretizations of evolution equations. Zbl 0968.65032 Gavrilyuk, I. P. 2 1999 A class of fully discrete approximations for the first order differential equations in Banach spaces with uniform estimates on the whole of \(\mathbb{R}^+\). Zbl 0961.65052 Gavrilyuk, Ivan P. 1 1999 Exact and approximate solutions of some operator equations based on the Cayley transform. Zbl 0938.47013 Gavrilyuk, Ivan P.; Makarov, Vladimir L. 4 1998 Representation and approximation of the solution of an initial value problem for a first order differential equation in Banach spaces. Zbl 0849.65040 Gavrilyuk, I. P.; Makarov, V. L. 15 1996 An algorithmic representation of fractional powers of positive operators. Zbl 0860.47011 Gavrilyuk, Ivan P. 9 1996 Representation and approximation of solutions of initial value problems for differential equations in Hilbert space based on the Cayley transform. Zbl 0828.34045 Arov, D. Z.; Gavrilyuk, I. P.; Makarov, V. L. 8 1995 The Cayley transform and the solution of an initial value problem for a first order differential equation with an unbounded operator coefficient in Hilbert space. Zbl 0802.47049 Gavrilyuk, Ivan P.; Makarov, Vladimir L. 11 1994 A method for solving initial value problems for linear differential equations in Hilbert space based on the Cayley transform. Zbl 0798.34064 Arov, Damir Z.; Gavrilyuk, Ivan P. 12 1993 Exact difference schemes and difference schemes of arbitrary given degree of accuracy for generalized one-dimensional third boundary value problems. Zbl 0779.65047 Gawrilyuk, I. P. 2 1993 Difference schemes for a fourth order one-dimensional equation with the nonlinear boundary condition. Zbl 0711.65061 Gavrilyuk, I. P.; Grekov, L. D. 1 1989 An exact and truncated difference schemes for boundary value problems with degeneration. Zbl 0579.65076 Gavrilyuk, I. P.; Luzhnykh, V. M.; Makarov, V. L. 1 1985 Convergence of finite-difference solutions to generalized solutions of the first boundary-value problem for a fourth-order quasilinear equation in regions of arbitrary shape. Zbl 0601.65072 Vojtsekhovskij, S. A.; Gavrilyuk, I. P. 1 1985 Estimates of the rate of convergence of difference schemes for fourth- order elliptic equations. Zbl 0541.65064 Gavrilyuk, I. P.; Lazarov, R. D.; Makarov, V. L.; Pirnazarov, S. P. 4 1983 Compatible estimates for the rate of convergence of difference solutions to generalized solutions of the first boundary value problem for fourth order equations. Zbl 0541.65062 Gavrilyuk, I. P.; Makarov, V. L.; Pirnazarov, S. P. 2 1983 Consistent estimates for the speed of convergence of difference solutions to generalized solutions of the first boundary-value problem for fourth order equations. Zbl 0566.65071 Gavrilyuk, I. P.; Makarov, V. L.; Pirnazarov, S. P. 1 1983 Ein exaktes Differenzenschema und abgeschnittene Differenzenschemata für eine gewisse Klasse Sturm-Liouvillescher Probleme mit Entartung. Zbl 0438.65071 Makarov, V. L.; Gavrilyuk, I. P.; Luzhnykh, V. M. 4 1980 Economic method for solving boundary value problems for a class of quasilinear equations containing the Laplace operator. Zbl 0474.35009 Gavrilyuk, I. P. 1 1980 all cited Publications top 5 cited Publications all top 5 Cited by 281 Authors 43 Makarov, Volodymyr Leonidovych 37 Gavrilyuk, Ivan P. 29 Khoromskiĭ, Boris Nikolaevich 14 Timokha, Alexander N. 13 Ashyralyev, Allaberen 13 Hackbusch, Wolfgang 12 Kutniv, Myroslav V. 9 Khoromskaia, Venera 9 Mayko, Nataliya Valentynivna 7 Vabishchevich, Pëtr Nikolaevich 6 Kressner, Daniel 6 Lukovsky, Ivan Oleksandrovych 5 Chapko, Roman 5 Dragunov, Denys V. 5 Faltinsen, Odd Magnus 5 Hermann, Martin 5 Lanzara, Flavia 5 López-Fernández, María 5 Romanyuk, Nataliia Mykolaivna 5 Schmidt, Gunther 4 Grasedyck, Lars 4 Kunynets’, A. V. 4 Massei, Stefano 4 Maz’ya, Vladimir Gilelevich 4 Ryabichev, Vyacheslav L. 4 Vasylyk, Vitaliĭ Borysovych 4 Weideman, J. André C. 3 Bilenko, V. I. 3 Bozhonok, K. V. 3 Dal, Fadime 3 Dzyadyk, S. Yu. 3 Guglielmi, Nicola 3 Kemmochi, Tomoya 3 Lapinska-Chrzczonowicz, Magdalena 3 Melnik, Roderick V. Nicholas 3 Oseledets, Ivan Valer’evich 3 Robol, Leonardo 3 Schweiger, Florian 3 Sheen, Dongwoo 3 Trotsenko, Yuriy 3 Tyrtyshnikov, Evgeniĭ Evgen’evich 3 Wang, Jiadong 3 Yurtsever, Hasan Ali 3 Zhou, Ding 2 Alyoubi, Ahmad 2 Bachmayr, Markus 2 Boĭchuk, Oleksandr Andriĭovych 2 Bonito, Andrea 2 Bora, Swaroop Nandan 2 Börm, Steffen 2 Chernova, M. O. 2 Colbrook, Matthew J. 2 Dahmen, Wolfgang A. 2 Espig, Mike 2 Ganesh, Mahadevan 2 Khomenko, N. V. 2 Koksal, Mehmet Emir 2 Kopachevskiĭ, Nikolaĭ Dmitrievich 2 Lazarov, Raytcho D. 2 Lin, Gao 2 Litsarev, Mikhail S. 2 Liu, Jun 2 Manucci, Mattia 2 Matus, Pëtr Paŭlavich 2 McLean, William 2 Melenk, Jens Markus 2 Müller, Stefan 2 Palencia, Cesar 2 Pasciak, Joseph E. 2 Pinar, Zehra 2 Piskarëv, S. I. 2 Rossokhata, Nataliya O. 2 Saghi, Hassan 2 Schneider, Reinhold 2 Schwab, Christoph 2 Shevtsova, Valentina M. 2 Simoncini, Valeria 2 Sitshaeva, Zera Zeker’yaevna 2 Soe, A. N. 2 Süli, Endre E. 2 Sun, Ying 2 Thomée, Vidar 2 Tobler, Christine 2 Trefethen, Lloyd Nicholas 2 Yasnou, V. 2 Ye, Wenbin 1 Agarwal, Ravi P. 1 Aggez, Necmettin 1 Ahmadi-Asl, Salman 1 Andreev, Roman 1 Anh, Vo V. 1 Ashyralyyev, Charyyar 1 Ayton, Lorna J. 1 Ballani, Jonas 1 Bandyrskii, B. I. 1 Banjai, Lehel 1 Barker, Andrew T. 1 Baumann, Gerd 1 Beik, Fatemeh Panjeh Ali 1 Benner, Peter ...and 181 more Authors all top 5 Cited in 86 Serials 15 Computational Methods in Applied Mathematics 14 Ukrainian Mathematical Journal 14 Journal of Mathematical Sciences (New York) 11 Mathematics of Computation 10 Journal of Computational and Applied Mathematics 8 Numerische Mathematik 7 Numerical Functional Analysis and Optimization 7 Applied Numerical Mathematics 6 Computers & Mathematics with Applications 6 Journal of Computational Physics 6 Journal of Engineering Mathematics 6 Cybernetics and Systems Analysis 6 SIAM Journal on Scientific Computing 6 Engineering Analysis with Boundary Elements 5 Journal of Fluid Mechanics 5 Applied Mathematics and Computation 5 Numerical Linear Algebra with Applications 4 SIAM Journal on Numerical Analysis 4 Numerical Methods for Partial Differential Equations 4 Journal of Integral Equations and Applications 4 Computational Mathematics and Mathematical Physics 4 Journal of Numerical Mathematics 3 Computer Physics Communications 3 BIT 3 Computing 3 Constructive Approximation 3 SIAM Journal on Matrix Analysis and Applications 3 Applied Mathematical Modelling 3 Linear Algebra and its Applications 3 Mathematical Problems in Engineering 3 Abstract and Applied Analysis 2 Fluid Dynamics 2 Journal of Scientific Computing 2 International Journal of Computer Mathematics 2 Applied and Computational Harmonic Analysis 2 Computing and Visualization in Science 2 Discrete Dynamics in Nature and Society 2 European Journal of Mechanics. B. Fluids 2 Engineering Computations 2 Acta Numerica 2 Nonlinear Oscillations 2 Annales Universitatis Mariae Curie-Skłodowska. Sectio A1. Informatica 1 Computer Methods in Applied Mechanics and Engineering 1 Journal of Mathematical Analysis and Applications 1 Physica A 1 Studia Mathematica 1 The Annals of Probability 1 Journal of Soviet Mathematics 1 Mathematics and Computers in Simulation 1 Zeitschrift für Analysis und ihre Anwendungen 1 Journal of Complexity 1 Applied Mathematics Letters 1 Mathematical and Computer Modelling 1 MCSS. Mathematics of Control, Signals, and Systems 1 Journal of Applied Mathematics and Stochastic Analysis 1 Numerical Algorithms 1 SIAM Review 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 St. Petersburg Mathematical Journal 1 Advances in Computational Mathematics 1 Matematychni Metody ta Fizyko-Mekhanichni Polya 1 European Journal of Control 1 Nonlinear Dynamics 1 Vietnam Journal of Mathematics 1 Fractional Calculus & Applied Analysis 1 The ANZIAM Journal 1 Differential Equations 1 Archives of Computational Methods in Engineering 1 Foundations of Computational Mathematics 1 Sādhanā 1 Central European Journal of Mathematics 1 Advances in Difference Equations 1 International Journal of Numerical Analysis and Modeling 1 Oberwolfach Reports 1 GAMM-Mitteilungen 1 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche 1 Communications in Computational Physics 1 Mathematical Modelling of Natural Phenomena 1 Ufimskiĭ Matematicheskiĭ Zhurnal 1 Journal of Computational and Graphical Statistics 1 International Journal of Advances in Engineering Sciences and Applied Mathematics 1 ISRN Mathematical Physics 1 Mathematics 1 AMM. Applied Mathematics and Mechanics. (English Edition) 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys 1 Bollettino dell’Unione Matematica Italiana all top 5 Cited in 32 Fields 192 Numerical analysis (65-XX) 76 Partial differential equations (35-XX) 58 Ordinary differential equations (34-XX) 40 Fluid mechanics (76-XX) 24 Linear and multilinear algebra; matrix theory (15-XX) 24 Operator theory (47-XX) 11 Approximations and expansions (41-XX) 11 Integral transforms, operational calculus (44-XX) 10 Integral equations (45-XX) 8 Systems theory; control (93-XX) 7 Real functions (26-XX) 7 Functional analysis (46-XX) 7 Mechanics of deformable solids (74-XX) 5 Probability theory and stochastic processes (60-XX) 5 Quantum theory (81-XX) 4 Potential theory (31-XX) 4 Special functions (33-XX) 4 Optics, electromagnetic theory (78-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 General and overarching topics; collections (00-XX) 3 Computer science (68-XX) 2 Functions of a complex variable (30-XX) 2 Difference and functional equations (39-XX) 2 Mechanics of particles and systems (70-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 History and biography (01-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Statistics (62-XX) 1 Operations research, mathematical programming (90-XX) 1 Biology and other natural sciences (92-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year