Raytcho Lazarov, Piotr Matus, Petr Vabishchevich
Modern Problems of Numerical Analysis. On the Centenary of the Birth of Alexander Andreevich Samarskii
Computational Methods in Applied Mathematics. 20 (2020), no. 4, pp.591-594.
https://doi.org/10.1515/cmam-2020-0108
Petr Vabishchevich
Incomplete iterative implicit schemes
Computational Methods in Applied Mathematics. 20 (2020), no. 4, pp.727-737.
https://doi.org/10.1515/cmam-2018-0295
P. N. Vabishchevich
Explicit–Implicit Schemes for First-Order Evolution Equations,
Differential Equations, 2020, Vol. 56, No. 7, pp. 882–889.
Raimondas Čiegis, Petr N.Vabishchevich
Two-level schemes of Cauchy problem method for solving fractional powers of elliptic operators
Computers & Mathematics with Applications. Volume 80, Issue 2, 15 July 2020, Pages 305-315.
https://doi.org/10.1016/j.camwa.2019.08.012
P. N. Vabishchevich
Approximation of a fractional power of an elliptic operator
Numer Linear Algebra Appl. 2020. Volume 27, Issue 3, e2287, P.1-14.
doi: 10.1002/nla.2287
Vasiliy V. Grigoriev, Oleg Iliev, Petr N. Vabishchevich
Computational Identification of Adsorption and Desorption Parameters for Pore Scale Transport in Random Porous Media
In: Lirkov I., Margenov S. (eds) Large-Scale Scientific Computing. LSSC 2019. Lecture Notes in Computer Science, vol 11958. Springer, p.115-122, 2020
doi: 10.1007/978-3-030-41032-2_12
P.N. Vabishchevich
Identification of a Time-Dependent Right-Hand Side of an Unsteady Equation with a Fractional Power of an Elliptic Operator
In: Lirkov I., Margenov S. (eds) Large-Scale Scientific Computing. LSSC 2019. Lecture Notes in Computer Science, vol 11958. Springer, p.105-112, 2020
doi: 10.1007/978-3-030-41032-2_11
Vasiliy V. Grigoriev, Oleg Iliev, Petr N. Vabishchevich,
Computational identification of adsorption and desorption parameters for pore scale transport in periodic porous media
Journal of Computational and Applied Mathematics, 370 (2020) 112661, 16 p.
https://doi.org/10.1016/j.cam.2019.112661
Raimondas Čiegis, Petr N. Vabishchevich
High order numerical schemes for solving fractional powers of elliptic operators
Journal of Computational and Applied Mathematics 372 (2020) 112627
A. O. Vasilev, A. V. Avvakumov, V. F. Strizhov and P. N. Vabishchevich
Numerical calculation of spectral problems in SP3 approximation by FEM
Journal of Physics: Conference Series, 2019, Volume 1392, 012076
doi:10.1088/1742-6596/1392/1/012076
A. E. Kolesov, D. Kh. Ivanov and P. N. Vabishchevich
Recovery of a piecewise constant lower coefficient of an elliptic equation
Journal of Physics: Conference Series, 2019, Volume 1392, 012084
doi:10.1088/1742-6596/1392/1/012084
D. Kh. Ivanov, A. E. Kolesov and P. N. Vabishchevich
Numerical method for recovering the piecewise constant right-hand side function of an elliptic equation from a boundary overdetermination data
Journal of Physics: Conference Series, 2019, Volume 1392, 012081
doi:10.1088/1742-6596/1392/1/012081
Alexander G. Churbanov, Petr N. Vabishchevich
Numerical solution of boundary value problems for the eikonal equation in an anisotropic medium
Journal of Computational and Applied Mathematics, 2019, Vol.362, P. 55-67
https://doi.org/10.1016/j.cam.2019.05.016
P. N. Vabishchevich
Computational Identification of the Time Dependence of the Right-Hand Side of a Hyperbolic Equation,
Computational Mathematics and Mathematical Physics, 2019, Vol. 59, No. 9, pp.1537-1545.
P. N. Vabishchevich
Three-Level Schemes for the Advection Equation,
Differential Equations, 2019, Vol. 55, No. 7, pp. 905–914.
Rafael Arutyunyan, Yuri Obukhov and Petr Vabishchevich
Numerical Simulation of Charged Fullerene Spectrum,
Mathematical Modelling and Analysis. 2019, Volume 24, Issue 2, 263–275.
Petr N. Vabishchevich
Identification of the Right-Hand Side of an Equation with a Fractional Power of an Elliptic Operator
G. Nikolov et al. (Eds.): NMA 2018, LNCS 11189, pp. 216–223, 2019.
https://doi.org/10.1007/978-3-030-10692-8_24
A. V. Avvakumov, V. F. Strizhov, P. N. Vabishchevich and A. O. Vasilev
Automatic Time Step Selection for Numerical Solution of Neutron Diffusion Problems
I. Dimov et al. (Eds.): FDM 2018, LNCS 11386, pp. 145–152, 2019.
https://doi.org/10.1007/978-3-030-11539-5_14
D. Kh. Ivanov and P. N. Vabishchevich
Iterative Process for Numerical Recovering the Lowest Order Space-Wise Coefficient in Parabolic Equations
I. Dimov et al. (Eds.): FDM 2018, LNCS 11386, pp. 289–296, 2019.
https://doi.org/10.1007/978-3-030-11539-5_32
Alexander G. Churbanov and Petr N. Vabishchevich
Numerical Solving a Boundary Value Problem for the Eikonal Equation
I. Dimov et al. (Eds.): FDM 2018, LNCS 11386, pp. 28–34, 2019.
https://doi.org/10.1007/978-3-030-11539-5_3
P. N. Vabishchevich
Alternating Triangular Schemes for Second-Order Evolution Equations,
Computational Mathematics and Mathematical Physics, 2019, Vol. 59, No. 2, pp.266-274.
Petr N. Vabishchevich
Computational identification of the lowest spacewise dependent coefficient of a parabolic equation,
Applied Mathematical Modelling.Vol. 65, 2019, P. 361–376.
P. Vabishchevich and A. Vasilev
Algorithm of time step evaluation for numerical solution of boundary value problem for parabolic equations.
In: Application of Mathematics in Technical and Natural Sciences. 2018. AIP Conf. Proc. 2025, 100010-1–100010-7.
Rafael V. Arutyunyan, Petr N. Vabishchevich and Yuri N. Obukhov
Existence of a system of discrete volume-localized quantum levels for charged fullerenes.
Phys. Rev. B. Vol. 98, 2018, 155427, P.1-10.
Petr N. Vabishchevich
Fundamental mode exact schemes for unsteady problems,
Numerical Methods for Partial Differential Equations. Vol.34(6), 2018, P.2301-2315.
P. N. Vabishchevich and P. E. Zakharov
Numerical solution of time-dependent problems with different time scales,
Computational Mathematics and Mathematical Physics, 2018, Vol. 58, No. 10, pp.1552-1561.
Peter Minev, Petr N. Vabishchevich
Splitting schemes for the stress formulation of the incompressible Navier–Stokes equations.
Journal of Computational and Applied Mathematics. Vol. 344, 2018, P. 807–818.
Petr N. Vabishchevich
Decoupling schemes for predicting compressible fluid flows,
Computers and Fluids. Vol.171, 2018, P. 94–102.
Petr N. Vabishchevich
Numerical Solution of Time-Dependent Problems with a Fractional-Power Elliptic Operator,
Computational Mathematics and Mathematical Physics, 2018, Vol. 58, No. 3, pp.394-409.
Alexander V. Avvakumov, Valery F. Strizhov, Petr N. Vabishchevich, Alexander O. Vasilev
State change modal method for numerical simulation of dynamic processes in a nuclear reactor,
Progress in Nuclear Energy. Vol. 106, 2018, P. 240–261.
Petr N. Vabishchevich
Two-level schemes for the advection equation,
Journal of Computational Physics, 2018, Vol. 363, P.158-177.
P. Minev, S. Srinivasan, P.N. Vabishchevich
Flux formulation of parabolic equations with highly heterogeneous coefficients,
Journal of Computational and Applied Mathematics. 2018, Vol.340, pp.582-601.
P.N. Vabishchevich
Two-component domain decomposition scheme with overlapping subdomains for parabolic equations,
Journal of Computational and Applied Mathematics. 2018, Vol.340, pp.664-675.
Alexander G. Churbanov, Oleg Iliev, Valery F. Strizhov, Petr N. Vabishchevich
Numerical simulation of oxidation processes in a cross–flow around tube bundles,
Applied Mathematical Modelling. 2018, Vol. 59, pp. 251-271.
Peter Minev, Petr N. Vabishchevich
Splitting schemes for unsteady problems involving the grad-div operator
Applied Numerical Mathematics. 2018, Vol.124, pp.130–139.
A. V. Avvakumov, P. N. Vabishchevich, A. O. Vasilev, V. F. Strizhov
Solution of the 3D Neutron Diffusion Benchmark by FEM.
In: Lirkov I., Margenov S. (eds) Large-Scale Scientific Computing. LSSC 2017. Lecture Notes in Computer Science, vol 10665. Springer, pp.435-442, 2018.
Petr N. Vabishchevich
Two Classes of Vector Domain Decomposition Schemes for Time-Dependent Problems with Overlapping Subdomains.
In: Lirkov I., Margenov S. (eds) Large-Scale Scientific Computing. LSSC 2017. Lecture Notes in Computer Science, vol 10665. Springer, pp.85-92, 2018.
Petr N. Vabishchevich
Numerical Solution of Time-Dependent Problems with Fractional Power Elliptic Operator
Computational Methods in Applied Mathematics, 2018, vol.18, issue 1, p.111-128.
B. Jin, R. Lazarov, P. Vabishchevich
Preface: Numerical Analysis of Fractional Differential Equations
Computational Methods in Applied Mathematics, 2017, vol.17, issue 4, p.643-646.
P. N. Vabishchevich
Vector Domain Decomposition Schemes for Parabolic Equations.
Computational Mathematics and Mathematical Physics, 2017, Vol. 57, No. 9, pp. 1530-1547.
P. N. Vabishchevich, S. P. Varlamov, V. I. Vasiliev, M. V. Vasilieva, S. P. Stepanov
Numerical Simulation of the Temperature Dynamics of Railway Foundation Material in Permafrost.
Mathematical Models and Computer Simulations, 2017, Vol. 9, No. 3, pp. 292–304.
P. N. Vabishchevich
Iterative computational identification of a space-wise dependent source in parabolic equation.
Inverse Problems in Science and Engineering. 2017, Vol.25, No. 8, p.1168–1190.
Alexander E. Kolesov, Petr N. Vabishchevich
Splitting schemes with respect to physical processes for double-porosity poroelasticity problems.
Russian Journal of Numerical Analysis and Mathematical Modelling, Volume 32, Issue 2, p. 99-114, 2017.
P. N. Vabishchevich, A. O. Vasil’ev
Time Step Selection for the Numerical Solution of Boundary Value Problems for Parabolic Equations.
Computational Mathematics and Mathematical Physics, 2017, Vol. 57, No. 5, pp. 843–853.
Petr N. Vabishchevich
Factorized Schemes of Second-Order Accuracy for Numerically Solving Unsteady Problems.
Computational Methods in Applied Mathematics, 2017, vol. 17, issue 2, 323-335.
R. Lazarov, P. Vabishchevich
A numerical study of the homogeneous elliptic equation with fractional boundary conditions
Fractional Calculus and Applied Analysis, 2017, Vol. 20, No 2, pp. 337–351.
Vabishchevich P.N.
A Singularly Perturbed Boundary Value Problems with Fractional Powers of Elliptic Operators.
In: Dimov I., Faragó I., Vulkov L. (eds) Numerical Analysis and Its Applications. NAA 2016. Lecture Notes in Computer Science, vol 10187. Springer, pp.141-152, 2017.
Avvakumov A.V., Strizhov V.F., Vabishchevich P.N., Vasilev A.O.
Algorithms for Numerical Simulation of Non-stationary Neutron Diffusion Problems.
In: Dimov I., Faragó I., Vulkov L. (eds) Numerical Analysis and Its Applications. NAA 2016. Lecture Notes in Computer Science, vol 10187. Springer, pp.212-219, 2017.
Kolesov A.E., Sivtsev P.V., Smarzewski P., Vabishchevich P.N.
Numerical Analysis of Reinforced Concrete Deep Beams.
In: Dimov I., Faragó I., Vulkov L. (eds) Numerical Analysis and Its Applications. NAA 2016. Lecture Notes in Computer Science, vol 10187. Springer, pp. 414-421, 2017.
Kolesov A.E., Vabishchevich P.N.
Numerical Solution of Thermoporoelasticity Problems.
In: Dimov I., Faragó I., Vulkov L. (eds) Numerical Analysis and Its Applications. NAA 2016. Lecture Notes in Computer Science, vol 10187. Springer, pp. 422-429, 2017.
Stepanov S.P., Sirditov I.K., Vabishchevich P.N., Vasilyeva M.V., Vasilyev V.I., Tceeva A.N.
Numerical Simulation of Heat Transfer of the Pile Foundations with Permafrost.
In: Dimov I., Faragó I., Vulkov L. (eds) Numerical Analysis and Its Applications. NAA 2016. Lecture Notes in Computer Science, vol 10187. Springer, pp. 625-632, 2017.
Su L., Vabishchevish P.N., Vasil’ev V.I.
The Inverse Problem of the Simultaneous Determination of the Right-Hand Side and the Lowest Coefficients in Parabolic Equations.
In: Dimov I., Faragó I., Vulkov L. (eds) Numerical Analysis and Its Applications. NAA 2016. Lecture Notes in Computer Science, vol 10187. Springer, pp. 633-639, 2017.
P. N. Vabishchevich, S. P. Varlamov, V. I. Vasiliev, M. V. Vasilieva and S. P. Stepanov
Numerical simulation of the temperature dynamics of railway foundation material in permafrost
Mathematical Models and Computer Simulations, 2017, Vol. 9, No. 3, pp. 292–304.
A. V. Avvakumov, P. N. Vabishchevich, A. O. Vasilev, and V. F. Strizhov
Spectral properties of dynamic processes in a nuclear reactor
Annals of Nuclear Energy. 2017, Vol. 99, pp.68-79.
O. P. Iliev, A. E. Kolesov, P. N. Vabishchevich
Numerical Solution of Plate Poroelasticity Problems.
Transport in Porous Media. 2016, Volume 115, Issue 3, pp 563–580
P. N. Vabishchevich, V. I. Vasil’ev, M. V. Vasil’eva and D. Ya. Nikiforov
Numerical Solution of an Inverse Filtration Problem
Lobachevskii Journal of Mathematics, 2016, Vol. 37, No. 6, pp. 777–786.
A. V. Avvakumov, P. N. Vabishchevich, A. O. Vasilev, and V. F. Strizhov
Solution of the neutronics code dynamic benchmark by finite element method
In: AIP Conference Proceedings 1773, 110003-1 - 110003-8 (2016).
S. V. Lemeshevsky, S. A. Naumovich, S. S. Naumovich, P. N. Vabishchevich, and P. E. Zakharov
Numerical simulation of the stress-strain state of the dental system
In: AIP Conference Proceedings 1773, 020004-1 - 020004-13 (2016).
P. N. Vabishchevich, M. V. Klibanov
Numerical identification of the leading coefficient of a parabolic equation.
Differential Equations. 2016, Vol. 52, No. 7, pp 855–862.
A.G. Churbanov, P.N. Vabishchevich
Numerical investigation of a space-fractional model of turbulent fluid flow in rectangular ducts.
J. Comput. Phys. 2016, Vol. 321, pp.846-859
P.N. Vabishchevich, P.E. Zakharov
Alternating Triangular Schemes for Convection–Diffusion Problems.
Computational Mathematics and Mathematical Physics, 2016, Vol. 56, No. 4, pp. 576–592.
Petr N. Vabishchevich
Numerical Solving Unsteady Space-Fractional Problems with the Square Root of an Elliptic Operator.
Mathematical Modelling and Analysis, 2016, Vol.21, No.2, pp. 220-238.
Petr N. Vabishchevich
Numerical solution of nonstationary problems for a space-fractional diffusion equation.
Fractional Calculus and Applied Analysis, 2016, Vol.19, No.1, pp. 116-139.
Petr N. Vabishchevich
A Splitting Scheme to Solve an Equation for Fractional Powers of Operators.
Computational Methods in Applied Mathematics, 2016, Vol.16, No.1, pp. 161-174.
P.N. Vabishchevich, A.V. Grigoriev
Numerical modeling of fluid flow in anisotropic fractured porous media.
Numerical Analysis and Applications, 2016, Vol.9, No.1, pp. 45-56.
P. Vabishchevich, V.I. Vasil’ev
Computational algorithms for solving the coefficient inverse problem for parabolic equations.
Inverse Problems in Science and Engineering, 2016, Vol. 24, No. 1, pp. 42-59.
P. Vabishchevich
Numerical solution of nonstationary problems for a convection and a space-fractional diffusion equation.
Journal of Numerical Analysis and Modeling, 2016, Vol. 13, No. 2, pp. 292-305.