Bücher

• Gavrilyuk, I.P., Makarov, V.L.: Strongly Positive Operators and Numerical Algorithms without Accuracy Saturation. Kiev 2004, Publishing House of the Institute of Mathematics of NASU. 499pp. (ISBN 966-02-3602-6). (in Russian).
• Gavrilyuk, I.P., Lukovsky, I.A., Makarov, V.L., Timokha, A.N.: Evolutional Problems of the Contained Fluid. Mathematical and Numerical Aspects. Kiev 2006, Publishing House of the Institute of Mathematics of NASU. 230pp. (ISBN 966-02-3949-1)
• Gavrilyuk, I., Hermann, M., Lukovsky, I., Makarov, V., Timokha, A.N.: Multidimensional Modal Systems of the Liquid Sloshing Dynamics and Their Numerical Analysis. (under preparation)

Artikel in referierten Zeitschriften

• Gavrilyuk, I.P.: Algorithms without accuracy saturation and exponential convergent algorithms for operator equations. Journal of Numerical and Applied Mathematics, 88 (2003), No. 1, 28-43
• Gavrilyuk, I., Timokha, A.N.: A Nyström-Kress scheme for a Dirichlet-Neumann boundary value problem associated with fluid sloshing in a rectangular tank. Proceeding of the Institute of Mathematics of NASU, 47 (2003), 284-301
• Gawriljuk, I., Hermann, M., Timokha, A.N.: Objektorientierte Computermodellierung -- die Technologie der Gegenwart und der Zukunft. Beiträge der Berufsakademie Thüringen, Heft 1 (2003), 88-97
• Gavrilyuk, I., Makarov, V., Rjabichev, V.: A parallel method of high accuracy for the first order evolution equation in Hilbert and Banach spaces. Computational Methods in Applied Mathematics, 3 (2003), No. 1, 86-115
• Gavrilyuk, I., Lukovsky, I., Timokha, A.N: Two-dimensional variational vibroequilibria and Faraday's drops. ZAMP, 55 (2004), 1015-1033
• Lukovsky, I.O.: Variational methods of investigation of the dynamics of solid bodies with liquid. International Applied Mechanics, 40 (2004), No. 10, 37-77
• Lukovsky, I.O., Solodun, A.: Investigations of the forced nonlinear sloshing in circular cylindrical tanks by means of seven-modes model of the third-order. Proceeding of the Institute of Mathematics of NASU, 47 (2004), 161-179 (in Russian).
• Hermann, M., Timokha, A.N.: Secondary bifurcations in nonlinear modal system modelling the fluid sloshing. Transactions of the Institute of Mathematics of NASU, 1 (2004), No. 2, 210-228.
• Gavrilyuk, I.P., Makarov, V.L., Vasylyk, V.: A new estimate of the Sinc method for linear parabolic problems including the initial point. Computational Methods in Applied Mathematics, 4 (2004), No. 2, 163-179
• Beyer, K., Günther, M., Timokha, A.N.: Variational and finite element analysis of vibroequilibria. Computational Methods in Applied Mathematics, 4 (2004), No. 3, 290-323
• Makarov, V.L., Gavrilyuk, I.P., Kutniv, M.V., Hermann, M.: A two-point difference scheme of arbitrary given accuracy order for BVP for systems of first order nonlinear ODEs. Computational Methods in Applied Mathematics, 4 (2004), No. 4, 42-68
• Bandyrskii, B.I., Gavrilyuk, I.P., Lazurchak, I.I., Makarov, V.L.: Functional -discrete method (FD-method) for matrix Sturm-Liouville problems. Computational Methods in Applied Mathematics, 5 (2005), No. 4, 362-386
• Beyer, K., Günther, M.: Dynamical stability of compressible drops and stars. Mathematical Methods in Applied Sciences, 28 (2005), No. 7, 789-810
• Solodun, O.V.: Modelling the nonlinear liquid sloshing in truncetd conical tanks: derivation of a modal system. Transactions of the Institute of Mathematics of NASU, 2 (2005), No. 1, 309-319. (in Ukrainian)
• Timokha, A.N.: Planimetry of vibrocapillary equilibria at small wave numbers. International Journal of Fluid Mechanics Research, 32 (2005), No. 4, 454-487
• Trotsenko, V.A.: Effect of annular baffles on the suppressing of the liquid sloshing. Reports of NASU, No. 5 (2005), 51-57 (in Russian)
• Lukovsky, I.O.: A mathematical model of wave motions of a liquid in containers with inclined walls. Transactions of the Institute of Mathematics of NASU, 2 (2005), No. 1, 227-253. (in Russian)
• Lukovsky, I.O., Ovchinnikov, D.: An optimal third-order model for the problem on nonlinear sloshing in a cylindrical tank. Transactions of the Institute of Mathematics of NASU, 2 (2005), No. 1, 254-264. (in Ukrainian)
• Hermann, M., Timokha, A.N.: Modal modelling of the nonlinear resonant sloshing in a rectangular tank I: A single-dominant model. Mathematical Models and Methods in Applied Sciences, 15 (2005), No. 9, 1431-1458.
• Faltinsen, O.M., Rognebakke, O.F., Timokha, A.N.: Classification of three-dimensional nonlinear sloshing in a square-base tank with finite depth. Journal of Fluids and Structures, 20 (2005), No. 1, 81-103
• Faltinsen, O.M., Rognebakke, O.F., Timokha, A.N.: Resonant three-dimensional nonlinear sloshing in a square base basin. Part 2. Effect of higher modes, Journal of Fluid Mechanics, 523 (2005), 199-218
• Gavrilyuk, I., Lukovsky, I., Timokha, A.N.: Linear and nonlinear sloshing in a conical tank. Fluid Dynamics Research, 37 (2005), 399-429
• Gavrilyuk, I., Makarov, V.: Algorithms without accuracy saturation for evolution equations in Hilbert and Banach spaces. Mathemathics of Computations, 74 (2005), 555-583
• Gavrilyuk, I.P., Makarov, V.L.: Exponentially convergent algorithms for the operator exponential with applications to inhomogeneous problems in Banach spaces. SIAM Journal on Numerical Analysis, 43 (2005), No. 5, 2144-2171
• Gavrilyuk, I., Lukovsky, I.A., Trotsenko, Yu., Timokha, A.N.: Sloshing in a vertical circular cylindrical tank with an annular baffle. Part~1. Linear fundamental solutions. Journal of Engineering Mathematics, 54 (2006), No. 1, 71-88
• Trotsenko, Yu.V.: Frequencies and forms of vibrations of a cylindrical shell with an attached rigid body. J. Sound and Vibrations, 292 (2006), No. 3-5, 535-551
• Gavrilyuk, I., Hermann, M., Kutniv, M.V., Makarov, V.L.: Difference schemes for nonlinear BVPs using Runge-Kutta IVP-solvers. Advances in Difference Equations, Volume 2006 (2006), Article ID 12167, 29 pages doi:10.1155/ADE/2006/12167
• Gavrilyuk, I.P., Hermann, M., Timokha, A., Trotsenko, V.: Modeling of the eigenfield of a prestressed hyperelastic membrane encapsulating a liquid. Comput. Methods Appl. Math. 6 (2006), No. 4, 367-385
• Gavrilyuk, I.P., Hermann, M., Kutniv, M.V., Makarov, V.L.: Difference schemes for nonlinear BVPs on the semiaxis. Comput. Methods Appl. Math. 7 (2007), No. 1, 25-47
• Hermann, M., Milde, Th.: Computing eigenfunctions of singular points in nonlinear parametrized two-point BVPs. Applied Numerical Mathematics (2008), doi:10.1016/j.apnum.2008.03.010
• I. Gavrilyuk, M. Hermann, I. Lukovsky, O. Solodun and A. Timokha: Natural sloshing frequencies in rigid truncated conical tanks. Engineering Computations, vol. 25, no. 6, pp. 518-540, 2008
• M. Barnyak, I. Gavrilyuk, M. Hermann, A. Timokha: ''Analytical velocity potentials in cells with a rigid spherical wall''. Z. Angew. Math. Mech. 1-8 (2010)/DOI 10.1002/zamm.201000078
• I. P. Gavrilyuk, M. Hermann, M. V. Kutniv and V. L. Makarov: ''Two-point difference schemes of an arbitrary given order of accuracy for nonlinear BVPs'', Applied Mathematics Letters, vol. 23, no. 5, pp. 585-590, 2010
• I. P. Gavrilyuk, M. Hermann, Yu. Trotsenko, A. Timokha: ''Eigenoscillations of three- and two-element flexible systems''. International Journal of Solids and Structures, no. 47, pp. 1857-1870, 2010

Vom Verlag angenommene Artikel

• Gavrilyuk, I., Lukovsky, I.A., Trotsenko, Yu., Timokha, A.N.: Sloshing in a vertical circular cylindrical tank with an annular baffle. Part~2. Nonlinear analysis. Journal of Engineering Mathematics. 32 pp.
• Lukovsky, I., Ovchinnikov, D.: Investigations of the forced nonlinear oscillations of a fluid in a cylindrical cavity utilising the five-order model of the smallness. Proceeding of the Institute of Mathematics of NASU, 25 pp.
• Lukovsky, I.A., Solodun, A., Timokha, A.N.: Natural liquid sloshing in truncated conical tanks. Acoustic Bulletin (in Russian)
• Hermann, M., Timokha, A.N.: Modal modelling of the nonlinear resonant fluid sloshing in a rectangular tank II: Secondary resonance. Mathematical Models and Methods in Applied Sciences, 23 pp.

Zur Publikation in Fachzeitschriften eingereichte Manuskripte

• Bohonova, T.Ju., Gavrilyuk, I.P., Makarov, V.L., Vasylyk, V.: Exponentially convergent Duhamel's like algorithms for differential equations with an operator coefficient possessing a variable domain in Banach space. SIAM J. Numer. Anal.
• Faltinsen, O.M., Rognebakke, O.F., Timokha, A.N.: Two-dimensional resonant piston-like sloshing in a moonpool. Linear inviscid statement. Journal of Fluid Mechanics
• Gavrilyuk, I.P., Hermann, M., Kutniv M.V., Makarov, V.L.: Adaptive Algorithms Based on Exact Difference Schemes for Nonlinear BVPs on the Half-Axis. Applied Numerical Mathematics
• Gavriljuk, I.P., Makarov, V.L.: An exponencial convergent algorithm for nonlinear differential equations in Banach spaces. Mathematics of Computations
• Trotsenko, Yu.: Natural oscillations of a shell of revolutions with an attached solid body at the end. Transactions of the Institute of Mathematics of NASU

Manuskripte in Bearbeitung

• Gavriljuk, I.P., Hermann, M., Timokha, A., Trotsenko, V.: Linear oscillations of a stretched hyperelastic circular membrane encapsulating a sloshing liquid. Part 1. Theory. For: Mathematical Models and Methods in Applied Sciences
• Gavriljuk, I.P., Hermann, M., Timokha, A., Trotsenko, V.: Linear oscillations of a stretched hyperelastic circular membrane encapsulating a sloshing liquid. Part 1. Numerical methods. For: Mathematical Models and Methods in Applied Sciences
• Gavrilyuk, I., Lukovsky, I.A., Trotsenko, Yu., Timokha, A.N.: The fluid sloshing in a vertical circular cylindrical tank with an annular baffle. Part 3. Effect of vortex shedding. For: Journal Engineering Mathematics
• Lukovsky, I.A., Solodun, A., Timokha, A.N.: Nonlinear liquid sloshing in truncated conical tanks. For: Acoustic Bulletin
• Timokha, A.N., Trotsenko, V.A.: Modal theory of sloshing dynamics in a mobile cylindrical tank with a rigid-ring baffle. For: Journal of Fluids and Structures

Preprints

• Bohonova, T.Ju., Gavrilyuk, I.P., Makarov, V.L., Vasylyk, V.: Exponentially convergent Duhamel's like algorithms for differential equations with an operator coefficient possessing a variable domain in Banach space. Reports on Numerical Mathematics, Friedrich-Schiller-Universität Jena, No. 05-06, 2005
• Bandyrskii, B.I., Gavrilyuk, I.P., Lazurchak, I.I., Makarov, V.L.: An algorithm for matrix Sturm-Liouville problems based on a piece-wise constant perturbation of the differential operator. Reports on Numerical Mathematics,Friedrich-Schiller-Universität Jena, No. 05-07, 2005
• Gavrilyuk, I.: Exponential convergent algorithm for differential equations. Berichte des IZWR, Interdisziplinäres Zentrum fuer Wissenschaftliches Rechnen, Jenaer Schriften zur Mathematik und Informatik, Band 1, 2003, 11-23
• Hermann, M., Kaiser, D.: Numerical methods for parametrized two-point boundary value problems - a survey. Berichte des IZWR, Interdisziplinäres Zentrum fuer Wissenschaftliches Rechnen, Jenaer Schriften zur Mathematik und Informatik, Band 1, 2003, 23-38
• Gavrilyuk, I.P., Hermann, M., Kutniv, M., Makarov, V.: Three-point difference schemes of variable order for nonlinear BVPs on the half-axis. Reports on Numerical Mathematics, , Friedrich-Schiller-Universität Jena, No. 05-04, 2005
• Gavrilyuk, I. P., Hermann, M., Kutniv, M., Makarov, V.: New methods for nonlinear BVPs on the half-axis using Runge-Kutta IVP-solvers. Reports on Numerical Mathematics, , Friedrich-Schiller-Universität Jena No. 05-18, 2005
• Gavriljuk, I.P., Hermann, M., Timokha, A., Trotsenko, V.: Linear oscillations of a stretched hyperelastic circular membrane encapsulating a sloshing liquid. Preliminary results. Reports on Numerical Mathematics, Friedrich-Schiller-Universität Jena, No. 05-19, 2005
• Gavrilyuk, I.P., Makarov, V.L.: An exponential convergent algorithm for nonlinear differential equations in Banach spaces. Reports on Numerical Mathematics , Jenaer Schriften zur Mathematik und Informatik, Friedrich-Schiller-Universität Jena, No. 02/05, 2005