P.N. Vabishchevich, V.I. Vasil’ev, M.V. Vasil’eva, D.Ya. Nikiforov.
Numerical Solution of an Inverse Problem of Filtration.
Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2015, vol. 157, no. 4, pp. 79-89. (In Russian)
Petr N. Vabishchevich
Operator-Difference Scheme with a Factorized Operator.
Large-Scale Scientific Computing 10th International Conference, LSSC 2015. Sozopol, Bulgaria, June 8–12, 2015, 2015, Springer, 2015, Pp. 72-79.
P.N. Vabishchevich, V.I. Vasil’ev
Numerically Solving the Identification Problem for the Lower Coefficient of a Parabolic Equation
Yakutian mathematical journal. V. 21, No 4 (84), 71-87, 2014.
Petr N. Vabishchevich, Petr E. Zakharov
Explicit-Implicit Splitting Schemes for Parabolic Equations and Systems.
Numerical Methods and Applications, Springer, 2015, Pp. 157-166.
Petr N. Vabishchevich
Time Step for Numerically Solving Parabolic Problems.
Finite Difference Methods,Theory and Applications. 6th International Conference, FDM 2014, Lozenetz, Bulgaria, June 18-23, 2014, Springer, 2015, Pp. 96-103.
Alexandr E. Kolesov, Petr N. Vabishchevich, Maria V. Vasilyeva, Victor F. Gornov
Splitting Scheme for Poroelasticity and Thermoelasticity Problems.
Finite Difference Methods,Theory and Applications. 6th International Conference, FDM 2014, Lozenetz, Bulgaria, June 18-23, 2014, Springer, 2015, Pp. 241-248.
Petr V. Sivtsev, Petr N. Vabishchevich, Maria V. Vasilyeva
Numerical Simulation of Thermoelasticity Problems on High Performance Computing Systems.
Finite Difference Methods,Theory and Applications. 6th International Conference, FDM 2014, Lozenetz, Bulgaria, June 18-23, 2014, Springer, 2015, Pp. 364-370.
Petr N. Vabishchevich, Maria V. Vasilyeva, Vasily I. Vasilyev
Computational Algorithm for Identification of the Right-Hand Side of the Parabolic Equation.
Finite Difference Methods,Theory and Applications. 6th International Conference, FDM 2014, Lozenetz, Bulgaria, June 18-23, 2014, Springer, 2015, Pp. 385-392.
V. Amirkhanov, M. Pavluš, T. P. Puzynina, I. V. Puzynin, I. Sarhadov, P. N. Vabishchevich
Scheme of splitting with respect to physical processes for a model of heat and moisture transfer
Physics of Particles and Nuclei Letters. 2015, Volume 12, Issue 3, pp 371-374.
P.N. Vabishchevich, V.I. Vasil'ev, M.V. Vasil'eva
Computational Identification of the Right-Hfnd Side of a Parabolic Equation
Computational Mathematics and Mathematical Physics, 2015, Vol. 55, No. 6, pp. 1015–1021.
Petr N. Vabishchevich
Numerically solving an equation for fractional powers of elliptic operators
Journal of Computational Physics. 2015, Vol. 282, No.1, pp. 289–302.
P. N. Vabishchevich, M. V. Vasilyeva, and N. V. Pavlova
Numerical Simulation of Thermal Stabilization of Filter Soils
Mathematical Models and Computer Simulations, 2015, Vol. 7, No. 2, pp. 154–164.
V. V. Belikov, N. P. Vabishchevich, P. N. Vabishchevich, U. V. Katishkov, and N. A. Mosunova
Material Property Database
Mathematical Models and Computer Simulations, 2015, Vol. 7, No. 2, pp. 95–102.
Petr N. Vabishchevich
A Priori Estimation of a Time Step for Numerically Solving Parabolic Problems
Mathematical Modelling and Analysis. 2015, Vol.20, No. 1, pp. 94-111.
P. N. Vabishchevich
Explicit schemes for parabolic and hyperbolic equations. Applied Mathematics and Computation 250 (2015) 424-431 (arxiv.org/abs/1310.4046).
P. A. Popov, P. N. Vabishchevich
Numerical simulation of the aluminum production
AIP Conference Proceedings 1629, 56-68 (2014).
Petr N. Vabishchevich
Additive schemes (splitting schemes) for some systems of evolutionary equations
Mathematics of Computation, 83 (290):2787-2797, 2014.
P.N. Vabishchevich, M.V. Vasilyeva, V. Gornov, N.V. Pavlova
Mathematical modeling of the artificial freezing of soils
Computational technologies. 2014. V. 19. № 4. P. 19-31.
P.N. Vabishchevich, M.V. Vasil'eva, A.E. Kolesov
Splitting Scheme for Poroelasticity and Thermoelasticity Problem
Computational Mathematics and Mathematical Physics, 2014, Vol. 54, No. 8, pp. 1305–1315.
N. M. Afanas'eva, P.N. Vabishchevich
Stable Difference Schemes for Certain Parabolic Equations
Computational Mathematics and Mathematical Physics, 2014, Vol. 54, No. 7, pp. 1159–1166.
P. N. Vabishchevich
Explicit Schemes for Parabolic Equations
Doklady Mathematics, 2014, Vol. 90, No. 1, pp. 429-431.
A.E. Kolesov, P.N. Vabishchevich, M.V. Vasilyeva
Splitting schemes for poroelasticity and thermoelasticity problems
Computers and Mathematics with Applications, 2014, Vol. 67, No.12, pp. 2185–2198.
Petr N. Vabishchevich, Vasily I. Vasil’ev
Computational algorithms for solving the coefficient inverse problem for parabolic equations
ICIPE2014 8th International Conference on Inverse Problems in Engineering, May 12–15, 2014, Poland. Eds: I. Szczygieł, A.J. Nowak, M. Rojczyk, Gliwice–Krakow, Poland, 2014, Pp.403-412.
P.N. Vabishchevich
Three Level Schemes of the Alternating Triangular Method
Computational Mathematics and Mathematical Physics, 2014, Vol. 54, No. 6, pp. 953–962.
P. N. Vabishchevich, V. I. Vasil’ev
Computational Determination of the Lowest Order Coefficient in a Parabolic Equation
Doklady Mathematics, 2014, Vol. 89, No. 2, pp. 179-181.
F. J. Gaspar, A. Grigoriev, P. Vabishchevich
Explicit-implicit splitting schemes for some systems of evolutionary equations
International Journal of Numerical Analysis and Modeling, 2014, Vol. 11, No. 2, pp. 346-357.
N. Boal, F. J. Gaspar, F. Lisbona, P. Vabishchevich
Stabilized Finite Difference Methods for the Fully Dynamic Biot's Problem
Mathematical Modelling and Analysis, 2013, Vol. 18, No. 4, pp. 463-479.
A.G. Churbanov, P.N. Vabishchevich
Numetical methods for solving convection-diffusion problems
Changying Zhao, editor, Focus on Porous Media Research, pp.1-83. Nova Science Publishers (2013) (arXiv:1208.5649).
Petr.N. Vabishchevich
Splitting schemes for hyperbolic heat conduction equation
BIT Numerical Mathematics. 2013, 53 (3), pp 755-778 (arXiv:1010.2412).
Nadezhda Afanasyeva, Petr N. Vabishchevich, Maria Vasilyeva
Unconditionally Stable Schemes for Non-stationary Convection-Diffusion Equations
I. Dimov, I. Farago, and L. Vulkov, editors, NAA 2012, LNCS 8236, pp. 151--157. Springer, Heidelberg (2013).
Petr N. Vabishchevich
Flux-Splitting Schemes for Parabolic Problems
I. Dimov, I. Farago, and L. Vulkov, editors, NAA 2012, LNCS 8236, pp. 132--142. Springer, Heidelberg (2013) (arXiv:1207.3450).
Petr Vabishchevich, Petr Zakharov
Domain Decomposition Scheme for First-Order Evolution Equations with Nonselfadjoint Operators
In: Numerical Solution of Partial Differential Equations: Theory, Algorithms, and Their Applications. Springer Proceedings in Mathematics & Statistics Volume 45, pp 279-302, 2013.
P.N. Vabishchevich
Flux-splitting schemes for parabolic equations with mixed derivatives
Computational Mathematics and Mathematical Physics, 2013, Vol. 53, No. 8, pp. 1139–1152.
P.N. Vabishchevich, A. V. Grigor’ev
Splitting schemes for pseudoparabolic equations
Differential Equations, 2013, Vol. 49, No. 7, pp. 807–814.
P.N. Vabishchevich, Iliev O.P.
Numerical Solution of NonStationary Problems for a System of Nernst–Planck Equationsa
Mathematical Models and Computer Simulations. Vol. 5, No. 3, pp. 229–243, 2013.
N. M. Afanas'eva, A.G. Churbanov,P.N. Vabishchevich
Unconditionally Monotone Schemes for Unsteady Convection-Diffusion Problems
Computational Methods in Applied Mathematics, 13(2):185-205, 2013.
N.M. Afanas’eva, P.N. Vabishchevich, M.V. Vasil’eva
Unconditionally Stable Schemes for Convection–Diffusion Problems
Russian Mathematics (Iz. VUZ), Vol. 57, No. 3, pp.1–11, 2013.
P.N. Vabishchevich
Operator-difference schemes for a class of systems of evolution equations
Mathematical Notes, Vol. 93, No. 1-2, pp.36-49, 2013.
P.N. Vabishchevich, M. Vasil'eva
Explicit-implicit schemes for convection-diffusion-reaction problems
Numerical Analysis and Applications, Vol. 5, No. 4, pp.297-306, 2012.
N. Boal, F. J. Gaspar, F. Lisbona, P. Vabishchevich
Finite Difference Analysis of a double porosity consolidation model
Numer. Methods Partial Differential Equations, 28(1): 138-154, 2012.
P.N. Vabishchevich
Domain decomposition methods for nonstationary problems
In: Proceeding of international conferences on mathematical modelling. Yakutsk, 2012, pp.232-243
P.N. Vabishchevich, M. Vasil'eva
Iterative Solution of the Pressure Problem for the Multiphase Filtration
Mathematical Modelling and Analysis, 2012, Vol.17, No.4, pp.532-549 (arXiv:1107.5479).
P.N. Vabishchevich
Domain decomposition schemes for the Stokes equation
Publications de l'Institut Mathematique, 2012, Vol. 91(105), pp.155-162 (arXiv:1102.0642).
P.N. Vabishchevich
Flux-.Splitting Schemes for Parabolic Problems
Computational Mathematics and Mathematical Physics, 2012, Vol. 52, No. 8, pp. 1128–1138.
V.S. Borisov, P.N. Vabishchevich, V.I. Vasil'ev, M.V. Vasil'eva, P.E. Zaharov, V.A. Kazakov
Development package SCore for numerical simulation on computer clusters
Vestnik CKR Rosnedra, 2, 36-39, 2012, in Russian.
P.N. Vabishchevich
SM-stability of operator-difference schemes
Computational Mathematics and Mathematical Physics, 2012, Vol. 52, No. 6, pp. 887–894.
N. Boal, F. J. Gaspar, F. Lisbona, P. Vabishchevich
Finite-Difference Analysis for the Linear Thermoporoelasticity Problem and Its Numerical Resolution by Multigrid Methods
Mathematical Modelling and Analysis, 2012, Vol. 17, No. 2, pp. 227–244.
P.N. Vabishchevich
Construction of Splitting Schemes Based on Transition Operator Approximation
Computational Mathematics and Mathematical Physics, 2012, Vol. 52, No. 2, pp. 253–262.
P. Vabishchevich
On a new class of additive (splitting) operator-difference schemes
Mathematics of Computation, 81(277):267-276, 2012 (arXiv:1005.2086).
P. Vabishchevich
SM stability for time-dependent problems
In I. Dimov, S. Dimova, and N. Kolkovska, editors, Numerical Methods and Applications. 7th International Conference, NMA 2010. Borovets, Bulgaria, August 20-24 2006. Revised Papers, volume 6046 of Lecture Notes in Computer Science, pages 29-40, Berlin, 2011. Springer (arXiv:1005.5712).
P.N. Vabishchevich
Two Level Schemes of Higher Approximation Order for Time Dependent Problems with Skew-Symmetric Operators
Computational Mathematics and Mathematical Physics, 2011, Vol. 51, No. 6, pp. 1050–1060.
P.N. Vabishchevich
Substructuring domain decomposition scheme for unsteady problems
Computational Methods in Applied Mathematics, 11(2):241-268, 2011 (arXiv:1105.3448).
N. Boal, F.J. Gaspar, F.J. Lisbona, P.N. Vabishchevich
Finite-difference analysis of fully dynamic problems for saturated porous media
Journal of Computational and Applied Mathematics, 236(6):1090-1102, 2011.