Vabishchevich P.N.
Operator-Difference Approximations on Two-Dimensional Merged Voronoi-Delaunay Grids
In: Samoylenko, I., Alikhanov, A., Kaplun, D., Lyakhov, P., Apekov, A. (eds) Current Problems of Applied Mathematics and Computer Systems. CPAMCS 2024. Lecture Notes in Networks and Systems, vol 1585. Springer, Cham, pp. 88-99, 2025
https://doi.org/10.1007/978-3-032-01831-1_9
Lomasov D., Vabishchevich P.
Iterative Solutions of the Incompressible Fluid Flow in a Lid-Driven Cavity at Large Reynolds Numbers
In: Samoylenko, I., Alikhanov, A., Kaplun, D., Lyakhov, P., Apekov, A. (eds) Current Problems of Applied Mathematics and Computer Systems. CPAMCS 2024. Lecture Notes in Networks and Systems, vol 1585. Springer, Cham, pp. 504-512, 2025
https://doi.org/10.1007/978-3-032-01831-1_47
P.N. Vabishchevich
Decomposition–Composition Schemes for Systems of Second-Order Evolution Equations
Computational Mathematics and Mathematical Physics, Vol. 65, no. 6, pp. 1195-1205
https://doi.org/10.1134/S0965542525700411
P.N. Vabishchevich
Decoupling technology for systems of evolutionary equations
Computers & Mathematics with Applications. Vol. 191, 2025, pp. 105-128
https://doi.org/10.1016/j.camwa.2025.04.022
Lomasov, Dmitri V. and Vabishchevich, Petr N.
Numerical solution of BVP for the incompressible Navier–Stokes equations at large Reynolds numbers
Russian Journal of Numerical Analysis and Mathematical Modelling, vol. 40, no. 4, 2025, pp. 281-295.
https://doi.org/10.1515/rnam-2025-0021
P.N. Vabishchevich
Computational decomposition and composition technique for approximate solution of nonstationary problem
Journal of Computational and Applied Mathematics 451 (2024) 116111
DOI: 10.1016/j.cam.2024.116111
P.N. Vabishchevich
Difference Operator Approximations on Nonstandard Rectangular Grid
Computational Mathematics and Mathematical Physics, 2024, Vol. 64, No. 7, pp. 1367–1380.
DOI: 10.1134/S0965542524700593
P.N. Vabishchevich
Splitting Schemes for Evolution Equations with a Factorized Operator
Differential Equations, 2024, Vol. 60, No. 7, pp. 868–876.
DOI: 10.1134/S0012266124070036
P.N. Vabishchevich
Splitting Schemes with Additive Representation of the Operator at the Time Derivative
Moscow University Computational Mathematics and Cybernetics, 2024, Vol. 48, No. 1, pp. 1–6.
DOI: 10.3103/S0278641924010096
P. N. Vabishchevich
Numerical-analytical Methods for Solving the Cauchy Problem for Evolutionary Equations with Memory
Lobachevskii Journal of Mathematics, 2023, Vol. 44, No. 10, pp. 4195–4204
https://doi.org/10.1134/S199508022310044X
P. N. Vabishchevich
Difference Decomposition Schemes Based on Splitting the Solution and Operator of the Problem,
Differential Equations, 2023, Vol. 59, No. 7, pp. 945–961.
https://doi.org/10.1134/S001226612307008X
P. N. Vabishchevich
Three-Level Schemes with Double Change in the Time Step
Computational Mathematics and Mathematical Physics, 2023, Vol. 63, No. 11, pp. 1989–1995
https://doi.org/10.1134/S0965542523110192
Petr N. Vabishchevich
Operator-difference schemes on non-uniform grids for second-order evolutionary equations
Russ. J. Numer. Anal. Math. Modelling 2023; 38(4):267–277
https://doi.org/10.1515/rnam-2023-0020
P.N. Vabishchevich
Nonlinear approximation of functions based on nonnegative least squares solver
Numerical Linear Algebra with Applications, 2023, Volume 30, Number 6, e2522, Pages 1–11
https://doi.org/10.1002/nla.2522
Petr N. Vabishchevich
Exponent splitting schemes for evolution equations with fractional powers of operators
International Journal Of Numerical Analysis And Modeling, 2023, Volume 20, Number 3, Pages 371–390
https://doi.org/10.4208/ijnam2023-1015
P. N. Vabishchevich
On Stability of an Approximate Solution of the Cauchy Problem for Some First-Order Integrodifferential Equations,
Comput. Math. and Math. Phys. 63, No. 2, 311–318 (2023)
https://doi.org/10.1134/S0965542523020124
P.N. Vabishchevich
Approximate solution of the Cauchy problem for a first-order integrodifferential equation with solution derivative memory.
Journal of Computational and Applied Mathematics. 2023, Volume 422, 114887, Pages 1–11
https://doi.org/10.1016/j.cam.2022.114887
Yalchin Efendiev, Wing Tat Leung, Wenyuan Li, Sai-Mang Pun, Petr N. Vabishchevich
Nonlocal transport equations in multiscale media. Modeling, dememorization, and discretizations,
Journal of Computational Physics,
Volume 472, 2023, 111555, pp. 1-77
https://doi.org/10.1016/j.jcp.2022.111555
P. N. Vabishchevich
Splitting Schemes for One Class of Operator Differential Equations,
Comput. Math. and Math. Phys. 62, 1033–1040 (2022)
https://doi.org/10.1134/S0965542522070107
P. N. Vabishchevich
Numerical Solution of the Cauchy Problem for a Second-Order Integro-Differential Equation,
Differential Equations, 2022, Vol. 58, No. 7, pp. 912–920.
https://doi.org/10.1134/S0012266122070047
Eric T. Chung, Yalchin Efendiev, Wing Tat Leung, Petr N. Vabishchevich
Contrast-independent partially explicit time discretizations for multiscale wave problems,
Journal of Computational Physics,
Volume 466, 2022, 111226, pp. 1-27
https://doi.org/10.1016/j.jcp.2022.111226
P.N. Vabishchevich
Numerical solution of the heat conduction problem with memory
Computers & Mathematics with Applications. Vol. 118, 15 July 2022, pp. 230-236
https://doi.org/10.1016/j.camwa.2022.05.020
Petr N. Vabishchevich
Factorized Schemes for First and Second Order Evolution Equations with Fractional Powers of Operators
Computational Methods in Applied Mathematics, vol. 22, no. 2, 2022, pp. 493-510.
https://doi.org/10.1515/cmam-2021-0073
P. N. Vabishchevich
Numerical Solution of Non-stationary Problems with a Rational Approximation for Fractional Powers of the Operator.
In: Lirkov, I., Margenov, S. (eds) Large-Scale Scientific Computing. LSSC 2021. Lecture Notes in Computer Science, vol 13127. Springer,
Pages 81-88, 2022
https://doi.org/10.1007/978-3-030-97549-4_9
P. N. Vabishchevich
Decoupling Methods for Systems of Parabolic Equations
In: Lirkov, I., Margenov, S. (eds) Large-Scale Scientific Computing. LSSC 2021. Lecture Notes in Computer Science, vol 13127. Springer,
Pages 287-294, 2022
https://doi.org/10.1007/978-3-030-97549-4_33
Vabishchevich P.N., Ivanov D.Kh.
Numerical computation of gravity force using solution of an auxiliary boundary value problem and the calculation of a surface integral
Computational Technologies, 2022, vol. 27, no. 1, pp. 21–38.
Petr N. Vabishchevich
Numerical solution of the Cauchy problem for Volterra integrodifferential equations with difference kernels.
Applied Numerical Mathematics. 2022, Volume 174, Pages 177-190
https://doi.org/10.1016/j.apnum.2022.01.013
Petr N. Vabishchevich
Some methods for solving equations with an operator function and applications for problems with a fractional power of an operator.
Journal of Computational and Applied Mathematics. 2022, Volume 407, 114096, Pages 1–13
https://doi.org/10.1016/j.cam.2022.114096
Petr N. Vabishchevich
Splitting schemes for some second-order evolutionary equations.
International Journal Of Numerical Analysis And Modeling. 2022, Volume 19, Number 1, Pages 19–32
V.V. Grigoriev, O. Iliev, P.N. Vabishchevich
On Parameter Identification for Reaction Dominated Pore-Scale Reactive Transport Using Modified Bee Colony Algorithm.
Algorithms 2022, 15(1), 15.
https://doi.org/10.3390/a15010015
D.Kh. Ivanov, A.E. Kolesov, P.N. Vabishchevich
Numerical method for solving the piecewise constant source inverse problem of an elliptic equation from a partial boundary observation data
Inverse and III-posed Problems 2019. Journal of Physics: Conference Series 2092 (2021) 012006, 9 p.
doi:10.1088/1742-6596/2092/1/012006
V.V. Grigoriev, P.N. Vabishchevich,
Bayesian Estimation of Adsorption and Desorption Parameters for Pore Scale Transport,
Mathematics, 2021, Vol. 9, No. 16, 1974, 16 p.
Eric T. Chung, Yalchin Efendiev, Wing Tat Leung, Petr N. Vabishchevich,
Contrast-independent partially explicit time discretizations for multiscale flow problems,
Journal of Computational Physics, Vol. 445, 2021, 110578, 21 p.
doi: 10.1016/j.jcp.2021.110578
P. N. Vabishchevich
Solution Decomposition Schemes for Second-Order Evolution Equations,
Differential Equations, 2021, Vol. 57, No. 7, pp. 848–856.
doi: 10.1134/S0012266121070028
D.K. Ivanov, P.N. Vabishchevich
Numerical solution of a boundary value problem with effective boundary conditions for calculation of gravity
Mathematical notes of NEFU, 202, Vol. 28, No 1, p.93-113
Yalchin Efendiev, Sai-Mang Pun, Petr N. Vabishchevich,
Temporal splitting algorithms for non-stationary multiscale problems,
Journal of Computational Physics, Vol. 439, 2021, 110375, 12p.
doi: 10.1016/j.jcp.2021.110375
Čiegis R., Vabishchevich P.
High-Order Two and Three Level Schemes for Solving Fractional Powers of Elliptic Operators.
In: Vermolen F.J., Vuik C. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2019. Lecture Notes in Computational Science and Engineering, vol 139. Springer, Cham. 2021
doi: 10.1007/978-3-030-55874-1_27
Petr N. Vabishchevich
Splitting schemes for non-stationary problems with a rational approximation for fractional powers of the operator
Applied Numerical Mathematics. Vol. 165, 2021, pp. 414-430
doi: 10.1016/j.apnum.2021.03.006
P.N. Vabishchevich
An approximate representation of a solution to fractional elliptical BVP via solution of parabolic IVP
Journal of Computational and Applied Mathematic. Vol. 391, 1 August 2021, article 113460, 13 p.
doi: 10.1016/j.cam.2021.113460
Yalchin Efendiev, Petr N. Vabishchevich
Splitting methods for solution decomposition in nonstationary problems
Applied Mathematics and Computation. Vol. 397, 15 May 2021, article 125785, 10 p.
doi: 10.1016/j.amc.2020.125785
A. Kurganov, P.N. Vabishchevich
Monotonization of a Family of Implicit Schemes for the Burgers Equation
In: Bock H.G., Jäger W., Kostina E., Phu H.X. (eds) Modeling, Simulation and Optimization of Complex Processes HPSC 2018. Springer, 2021, pp 247-256
doi: 10.1007/978-3-030-55240-4_12
P. N. Vabishchevich
Monotone schemes for convection–diffusion problems with convective transport in different forms,
Computational Mathematics and Mathematical Physics, 2021, Vol. 61, No. 1, 95-107.