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## Vabishchevich, Pëtr Nikolaevich

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 Author ID: vabishchevich.petr-n Published as: Vabishchevich, P. N.; Vabishchevich, Petr N.; Vabishchevich, Petr; Vabishchevich, Peter N.; Vabishchevich, P.; Vabischchevich, P. N.; Vabishchevich, P. W.; Vabishchevish, P. N.; Yabishchevich, P. N. Homepage: https://sites.google.com/site/vabishchevich/home External Links: Math-Net.Ru · dblp · GND
 Documents Indexed: 339 Publications since 1978, including 9 Books
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#### Co-Authors

 132 single-authored 59 Samarskiĭ, Aleksandr Andreevich 23 Matus, Pëtr Paŭlavich 17 Churbanov, Alexander G. 14 Lisbona Cortés, Francisco Javier 13 Gaspar, Francisco José 12 Iliev, Oleg P. 9 Vasil’ev, Vasiliĭ Ivanovich 8 Chudanov, Vladimir V. 8 Pulatov, P. A. 7 Pavlov, Andrei N. 7 Vasil’eva, Mariya V. 6 Gassiev, R. V. 6 Kolesov, Aleksandr Egorovich 5 Vabishchevich, T. N. 4 Boal, Natalia 4 Degtyarev, L. M. 4 Gabov, Sergei Aleksandrovich 4 Minev, Peter Dimitrov 4 Strizhov, Valery F. 4 Zakharov, Petr E. 3 Afanas’eva, Nadyezhda M. 3 Čiegis, Raimondas 3 Lazarov, Raytcho D. 3 Radzhabov, M. D. 3 Salaeva, T. V. 3 Vasilev, Aleksandr O. 3 Vasilyeva, Maria V. 3 Zyl, A. N. 2 Aksenova, A. E. 2 Avvakumov, A. V. 2 Borukhov, V. T 2 Denisenko, A. Yu. 2 Esikova, N. B. 2 Glasko, V. B. 2 Gornov, Victor F. 2 Grigor’ev, A. V. 2 Grigoriev, Vasiliy V. 2 Jovanović, Boško S. 2 Kriksin, Yu. A. 2 Lemeshevskiǐ, S. V. 2 Oosterlee, Cornelis Willebrordus 2 Pavlova, Nataliya V. 2 Pervichko, V. A. 2 Pulatov, S. I. 2 Semenov, V. K. 2 Shcheglik, V. S. 2 Shevtsov, P. V. 2 Shishkin, Grigoriĭ Ivanovich 2 Stepanov, Sergei P. 2 Vasenko, S. A. 2 Verakhovskij, V. A. 1 Abrashin, Vyacheslav Nikolaevich 1 Afanasyeva, Nadezhda 1 Ajryan, Eh. A. 1 Antonov, Mikhail Yu. 1 Arutyunyan, Rafael 1 Boyadjiev, Christo B. 1 Chernogorova, Tatiana P. 1 Chetverushkin, Boris Nikolaevich 1 Daniyarov, A. O. 1 Drozdov, V. V. 1 Efendiev, Yalchin R. 1 Egorov, Ivan Egorovich 1 Egorov, V. A. 1 Gabov, A. S. 1 Gorbachevskiĭ, A. Ya. 1 Gracia, José Luis 1 Grigor’ev, Yuri M. 1 Grigoriev, Alexander 1 Gulin, Alexei V. 1 Ivanov, D. Kh. 1 Ivanova, Anna Olegovna 1 Jin, Bangti 1 Klibanov, Michael V. 1 Lazarev, Nyurgun Petrovich 1 Makarevich, E. L. 1 Makarov, Mikhail M. 1 Naumovich, Anna 1 Nikiforov, D. Ya. 1 Obukhov, Yuri N. 1 Pavlush, M. 1 Popkov, A. G. 1 Popov, Sergey V. 1 Rychagov, V. G. 1 Sirditov, Ivan K. 1 Sivtsev, Petr Vasilievich 1 Smarzewski, Piotr 1 Srinivasan, Shriram 1 Su, LingDe 1 Tceeva, Anastasiya N. 1 Troeva, Marianna S. 1 Vabishchevich, N. P. 1 Varlamov, S. P. 1 Vasileva, Maria T. 1 Vulkov, Lubin G.
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#### Serials

 31 Matematicheskoe Modelirovanie 24 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 22 Differential Equations 21 Computational Mathematics and Mathematical Physics 15 Doklady Mathematics 15 Computational Methods in Applied Mathematics 14 U.S.S.R. Computational Mathematics and Mathematical Physics 11 Moscow University Computational Mathematics and Cybernetics 9 Journal of Computational and Applied Mathematics 9 Computational Mathematics and Modeling 8 Differential Equations 8 Mathematical Modelling and Analysis 7 Differentsial’nye Uravneniya 5 Soviet Mathematics. Doklady 4 Applied Numerical Mathematics 4 Russian Mathematics 3 Doklady Akademii Nauk Tadzhikskoĭ SSR 3 International Journal of Heat and Mass Transfer 3 Journal of Computational Physics 3 Soviet Mathematics 3 Numerical Methods for Partial Differential Equations 3 Doklady Akademii Nauk Belarusi 3 Vestnik Moskovskogo Universiteta. Seriya 15 2 Computers and Fluids 2 Computers & Mathematics with Applications 2 Computer Methods in Applied Mechanics and Engineering 2 Mathematics of Computation 2 Applied Mathematics and Computation 2 Communications in Applied Numerical Methods 2 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 2 Applied Mathematical Modelling 2 Fractional Calculus & Applied Analysis 2 Sibirskiĭ Zhurnal Vychislitel’noĭ Matematiki 2 Kragujevac Journal of Mathematics 2 HERMIS-$$\mu\pi$$. Hellenic European Research on Mathematics and Informatics Science 2 International Journal of Numerical Analysis and Modeling 1 Computer Physics Communications 1 International Journal for Numerical Methods in Fluids 1 Izvestiya Vysshikh Uchebnykh Zavedeniĭ, Matematika 1 Mathematical Notes 1 Moscow University Physics Bulletin 1 Journal of Theoretical and Applied Mechanics (Sofia) 1 BIT 1 Publications de l’Institut Mathématique. Nouvelle Série 1 Vestnik Moskovskogo Universiteta. Seriya III. Fizika, Astronomiya 1 Soviet Physics. Doklady 1 Vestsi Akadèmii Navuk Belarusi. Seryya Fizika-Matèmatychnykh Navuk 1 Mathematical Modeling and Computational Experiment 1 Numerical Linear Algebra with Applications 1 Journal of Inverse and Ill-Posed Problems 1 Russian Journal of Numerical Analysis and Mathematical Modelling 1 Obchyslyuval’na ta Prykladna Matematyka 1 Fundamental’naya i Prikladnaya Matematika 1 Vychislitel’nye Tekhnologii 1 Matematicheskie Zametki YAGU 1 Lobachevskii Journal of Mathematics 1 Doklady Natsional’noĭ Akademii Nauk Belarusi 1 Inverse Problems in Science and Engineering 1 Mathematics and its Applications (Dordrecht) 1 AIP Conference Proceedings 1 Inverse and Ill-Posed Problems Series 1 Matematicheskie Zametki SVFU
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#### Fields

 267 Numerical analysis (65-XX) 194 Partial differential equations (35-XX) 80 Fluid mechanics (76-XX) 24 Mechanics of deformable solids (74-XX) 23 Ordinary differential equations (34-XX) 20 Classical thermodynamics, heat transfer (80-XX) 11 Operator theory (47-XX) 8 Geophysics (86-XX) 6 Potential theory (31-XX) 5 General and overarching topics; collections (00-XX) 5 Real functions (26-XX) 4 Optics, electromagnetic theory (78-XX) 3 Approximations and expansions (41-XX) 3 Integral equations (45-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Biology and other natural sciences (92-XX) 1 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Functions of a complex variable (30-XX) 1 Difference and functional equations (39-XX) 1 Functional analysis (46-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Computer science (68-XX) 1 Quantum theory (81-XX)

#### Citations contained in zbMATH Open

156 Publications have been cited 683 times in 396 Documents Cited by Year
Difference schemes with operator factors. Zbl 1018.65103
Samarskii, A. A.; Matus, P. P.; Vabishchevich, P. N.
2002
Numerical methods for solving inverse problems of mathematical physics. Zbl 1136.65105
Samarskii, Alexander A.; Vabishchevich, Peter N.
2007
Additive operator-difference schemes. Splitting schemes. Zbl 1286.65105
Vabishchevich, Petr N.
2014
A finite difference analysis of Biot’s consolidation model. Zbl 1023.76032
Gaspar, F. J.; Lisbona, F. J.; Vabishchevich, P. N.
2003
Numerical solution of the inverse problem of reconstructing a distributed right-hand side of a parabolic equation. Zbl 0966.65067
Borukhov, V. T.; Vabishchevich, P. N.
2000
Numerically solving an equation for fractional powers of elliptic operators. Zbl 1352.65557
Vabishchevich, Petr N.
2015
Splitting schemes for poroelasticity and thermoelasticity problems. Zbl 1368.74062
Kolesov, A. E.; Vabishchevich, P. N.; Vasilyeva, M. V.
2014
Staggered grid discretizations for the quasi-static Biot’s consolidation problem. Zbl 1091.76047
Gaspar, F. J.; Lisbona, F. J.; Vabishchevich, P. N.
2006
An efficient multigrid solver for a reformulated version of the poroelasticity system. Zbl 1173.74460
Gaspar, F. J.; Lisbona, F. J.; Oosterlee, C. W.; Vabishchevich, P. N.
2007
Domain decomposition methods with overlapping subdomains for the time-dependent problems of mathematical physics. Zbl 1156.65084
Vabishchevich, P. N.
2008
Computational identification of the right-hand side of a parabolic equation. Zbl 1325.65136
Vabishchevich, P. N.; Vasil’ev, V. I.; Vasil’eva, M. V.
2015
Numerical solution of time-dependent problems with fractional power elliptic operator. Zbl 1383.65128
Vabishchevich, Petr N.
2018
Numerical simulation of convection/diffusion phase change problems – a review. Zbl 0790.76104
Samarskij, A. A.; Vabishchevich, P. N.; Iliev, O. P.; Churbanov, A. G.
1993
Numerical solution of nonstationary problems for a space-fractional diffusion equation. Zbl 1382.65330
Vabishchevich, Petr N.
2016
On a new class of additive (splitting) operator-difference schemes. Zbl 1251.65125
Vabishchevich, Petr N.
2012
Difference methods for solving mathematical physics problems on unstructured grids. Zbl 1090.65540
Samarskii, A. A.; Vabishchevich, P. N.
2000
The method of fictitious domains in problems of mathematical physics. (Metod fiktivnykh oblastej v zadachakh matematicheskoj fiziki.) Zbl 0787.65073
Vabishchevich, P. N.
1991
Additive difference schemes and iteration methods for problems of mathematical physics. Zbl 0985.65107
Samarskii, A. A.; Vabishchevich, P. N.
1997
A substructuring domain decomposition scheme for unsteady problems. Zbl 1283.65095
Vabishchevich, Petr
2011
Numerical identification of the leading coefficient of a parabolic equation. Zbl 1351.35087
Vabishchevich, P. N.; Klibanov, M. V.
2016
Finite-difference approximation of mathematical physics problems on irregular grids. Zbl 1118.65377
Vabishchevich, P. N.
2005
A numerical study of the homogeneous elliptic equation with fractional boundary conditions. Zbl 1364.65253
Lazarov, Raytcho; Vabishchevich, Petr
2017
Monotone finite-difference schemes on triangular grids for convection-diffusion problems. Zbl 1116.80304
Vabishchevich, P. N.; Samarskii, A. A.
2002
Operator-splitting methods for the incompressibel Navier-Stokes equations on non-staggered grids. I: First-order schemes. Zbl 0869.76052
Churbanov, Alexander G.; Pavlov, Andrei N.; Vabishchevich, Peter N.
1995
Parallel domain decomposition algorithms for time-dependent problems of mathematical physics. Zbl 0812.65088
Vabishchevich, P. N.
1994
Difference schemes with domain decomposition for solving non-stationary problems. Zbl 0719.65072
Vabishchevich, P. N.
1989
Operator-splitting schemes for solving elasticity problems. Zbl 1054.65096
Lisbona, F. J.; Vabishchevich, P. N.
2001
Explicit schemes for parabolic and hyperbolic equations. Zbl 1328.65185
Vabishchevich, P. N.
2015
Regularized additive operator-difference schemes. Zbl 1224.65213
Vabishchevich, P. N.
2010
Difference schemes for the transport equation. Zbl 1094.65082
Samarskii, A. A.; Vabishchevich, P. N.
2001
A numerical study on natural convection of a heat-generating fluid in rectangular enclosures. Zbl 0900.76599
Churbanov, A. G.; Vabishchevich, P. N.; Chudanov, V. V.; Strizhov, V. F.
1994
Finite difference schemes for poro-elastic problems. Zbl 1075.76600
Gaspar, F. J.; Lisbona, F. J.; Vabishchevich, P. N.
2002
Additive schemes for systems of time-dependent equations of mathematical physics. Zbl 1032.65097
Samarskii, Alexander; Vabishchevich, Petr
2003
Coefficient stability of operator-differential equations and operator-difference schemes. Zbl 1189.34107
Samarskiĭ, A. A.; Vabishchevich, P. N.; Matus, P. P.
1998
A stabilized method for a secondary consolidation Biot’s model. Zbl 1128.76043
Gaspar, F. J.; Gracia, J. L.; Lisbona, F. J.; Vabishchevich, P. N.
2008
Unconditionally monotone schemes for unsteady convection-diffusion problems. Zbl 1393.65006
Afanas’eva, Nadyezhda M.; Churbanov, Alexander G.; Vabishchevich, Petr N.
2013
Numerical investigation of a space-fractional model of turbulent fluid flow in rectangular ducts. Zbl 1349.76444
Churbanov, Alexander G.; Vabishchevich, Petr N.
2016
Flux-splitting schemes for parabolic problems. Zbl 1274.35160
Vabishchevich, P. N.
2012
Two-level finite difference scheme of improved accuracy order for time-dependent problems of mathematical physics. Zbl 1224.65184
Vabishchevich, P. N.
2010
Additive schemes for certain operator-differential equations. Zbl 1224.35328
Vabishchevich, P. N.
2010
Difference schemes for nonstationary vector problems. Zbl 1105.78016
Vabishchevich, P. N.
2004
Stability of three-layer difference schemes on grids that are nonuniform with respect to time. Zbl 1046.65077
Samarskij, A. A.; Vabishchevich, P. N.; Makarevich, E. L.; Matus, P. P.
2001
Difference schemes of increased order of approximation on nonuniform grids for elliptic equations. Zbl 1057.65512
Samarskiĭ, A. A.; Vabishchevich, P. N.; Matus, P. P.
1996
Minev, Peter; Vabishchevich, Petr N.
2018
Flux-splitting schemes for parabolic equations with mixed derivatives. Zbl 1299.35147
Vabishchevich, P. N.
2013
Explicit-implicit splitting schemes for some systems of evolutionary equations. Zbl 1310.65092
Gaspar, Francisco; Grigoriev, Alexander; Vabishchevich, Petr
2014
Two-level schemes for the advection equation. Zbl 1392.76032
Vabishchevich, Petr N.
2018
Numerical solution of nonstationary problems for a convection and a space-fractional diffusion equation. Zbl 1348.65119
Vabishchevich, Petr
2016
Splitting schemes with respect to physical processes for double-porosity poroelasticity problems. Zbl 1457.76100
Kolesov, Alexander E.; Vabishchevich, Petr N.
2017
Two-level schemes of Cauchy problem method for solving fractional powers of elliptic operators. Zbl 1446.65062
Čiegis, Raimondas; Vabishchevich, Petr N.
2020
Unconditionally stable schemes for convection-diffusion problems. Zbl 1268.76040
Afanas’eva, N. M.; Vabishchevich, P. N.; Vasil’eva, M. V.
2013
Difference scheme of the second order of accuracy for Dirichlet problem in arbitrary domain. Zbl 1063.65575
Samarskij, A. A.; Vabishchevich, P. N.; Zyl’, A. N.; Matus, P. P.
1999
Finite-difference analysis of fully dynamic problems for saturated porous media. Zbl 1375.76106
Boal, N.; Gaspar, F. J.; Lisbona, F. J.; Vabishchevich, P. N.
2011
Finite difference analysis of a double-porosity consolidation model. Zbl 1373.76157
Boal, N.; Gaspar, F. J.; Lisbona, F. J.; Vabishchevich, P. N.
2012
Finite-difference analysis for the linear thermoporoelasticity problem and its numerical resolution by multigrid methods. Zbl 1238.74012
Boal, Natalia; Gaspar, Francisco José; Lisbona, Francisco; Vabishchevich, Petr
2012
Computational determination of the lowest order coefficient in a parabolic equation. Zbl 1301.65103
Vabishchevich, P. N.; Vasil’ev, V. I.
2014
Three-level schemes of the alternating triangular method. Zbl 1313.35175
Vabishchevich, P. N.
2014
Operator-splitting schemes for the stream function-vorticity formulation. Zbl 0846.76058
Chudanov, V. V.; Popkov, A. G.; Churbanov, A. G.; Vabishchevich, P. N.; Makarov, M. M.
1995
Finite difference methods: theory and applications. Proceedings of the 1st conference on finite difference methods held in Rousse, Bulgaria, August 10–13, 1997. Zbl 0954.00042
Samarskiĭ, A. A. (ed.); Vabishchevich, Petr N. (ed.); Vulkov, Lubin G. (ed.)
1999
Parallel domain decomposition algorithms for parabolic problems. Zbl 1071.65546
Vabishchevich, P. N.
1997
Iterative solution of a retrospective inverse problem of heat conduction. Zbl 1071.80505
Samarskiĭ, A. A.; Vabishchevich, P. N.; Vasil’ev, V. I.
1997
Finite difference schemes for convection-diffusion problems on irregular meshes. Zbl 0993.76058
Vabishchevich, P. N.; Samarskij, A. A.
2000
Problems in compressible fluid dynamics with a variable viscosity. Zbl 0998.76065
Vabishchevich, P. N.; Samarskij, A. A.
2000
Vector additive difference schemes for first-order evolution equations. Zbl 1159.65328
Vabishchevich, P. N.
1996
Implicit finite-difference schemes for the nonstationary Navier-Stokes equations with the stream function and the vorticity as variables. Zbl 0654.76022
Vabishchevich, P. N.
1984
Regularized additive full approximation schemes. Zbl 0959.65099
Samarskij, A. A.; Vabishchevich, P. N.
1998
Approximation of a fractional power of an elliptic operator. Zbl 07217193
Vabishchevich, P. N.
2020
Splitting schemes for hyperbolic heat conduction equation. Zbl 1278.65128
Vabishchevich, Petr N.
2013
SM-stability of operator-difference schemes. Zbl 1274.65260
Vabishchevich, P. N.
2012
Stability of solutions of differential-operator and operator-difference equations in the sense of perturbation of operators. Zbl 1119.34046
Jovanović, B. S.; Lemeshevsky, S. V.; Matus, P. P.; Vabishchevich, P. N.
2006
Numerical solution of problems of identification of the right-hand side of a parabolic equation. Zbl 1074.65111
Vabishchevich, P. N.
2003
Splitting scheme for poroelasticity and thermoelasticity problems. Zbl 1313.74033
Vabishchevich, P. N.; Vasil’eva, M. V.; Kolesov, A. E.
2014
Reconstruction of the right-hand side of the elliptical equation from observation data obtained at the boundary. Zbl 1199.65373
Vabishchevich, Petr N.
2007
Regularized difference schemes for evolutionary second order equations. Zbl 0763.65073
Samarskii, Aleksandr A.; Vabishchevich, Peter N.
1992
On a numerical solution of non-local elliptic problems. Zbl 0533.65076
Vabishchevich, P. N.
1983
A numerical solution method for the Cauchy problem for elliptic equations. Zbl 0553.65061
Vabishchevich, P. N.; Pulatov, P. A.
1984
Nonlocal parabolic problems and the inverse heat-conduction problem. Zbl 0556.35064
Vabishchevich, P. N.
1982
Regionally additive difference schemes with a stabilizing correction for parabolic problems. Zbl 0838.65086
Vabishchevich, P. N.
1994
Vector additive schemes for second-order evolution equations. Zbl 0951.65081
Abrashin, V. N.; Vabishchevich, P. N.
1998
Difference schemes for the transport equation. Zbl 0944.65098
Samarskii, A. A.; Vabishchevich, P. N.
1998
Second-order accurate finite-difference schemes on nonuniform grids. Zbl 0951.65103
Vabishchevich, P. N.; Samarskij, A. A.; Matus, P. P.
1998
Two-level difference schemes with variable weights. Zbl 0804.65095
Vabishchevich, P. N.; Matus, P. P.
1993
Numerical solution of boundary value problems for fourth order elliptic equations. Zbl 0598.65079
Vabishchevich, P. N.
1984
Numerical solution of the exterior Neumann problem. Zbl 0625.65111
Vabishchevich, P. N.; Pulatov, P. A.
1987
Numerical methods for the solution of free boundary problems. (Chislennye metody resheniya zadach so svobodnoj granitsej). Zbl 0629.65129
Vabishchevich, P. N.
1987
Numerical solution of an inverse problem of source reconstructions in a parabolic equation. Zbl 1189.65234
Borukhov, V. T.; Vabishchevich, P. N.
1998
Regularized difference schemes for equations with nonselfadjoint operators. Zbl 1189.65201
Samarskiĭ, A. A.; Vabishchevich, P. N.
1992
On numerical solution of 1D poroelasticity equations in a multilayered domain. Zbl 1083.74051
Naumovich, A.; Iliev, O.; Gaspar, F.; Lisbona, F.; Vabishchevich, P.
2005
Difference schemes with variable weights for second order evolution equations. Zbl 0819.65093
Vabishchevich, P. N.; Matus, P. P.; Shcheglik, V. S.
1994
Interpolation finite difference schemes on grids locally refined in time. Zbl 0978.65078
Shishkin, G. I.; Vabishchevich, P. N.
2000
Explicit-implicit schemes for convection-diffusion-reaction problems. Zbl 1299.65198
Vabishchevich, P. N.; Vasil’eva, M. V.
2012
Time step for numerically solving parabolic problems. Zbl 1359.65131
Vabishchevich, Petr N.
2015
Flux formulation of parabolic equations with highly heterogeneous coefficients. Zbl 1432.65132
Minev, Peter; Srinivasan, Shriram; Vabishchevich, Petr N.
2018
Explicit-implicit splitting schemes for parabolic equations and systems. Zbl 1360.65219
Vabishchevich, Petr N.; Zakharov, Petr E.
2015
Numerical simulation of oxidation processes in a cross-flow around tube bundles. Zbl 07167908
Churbanov, Alexander G.; Iliev, Oleg; Strizhov, Valery F.; Vabishchevich, Petr N.
2018
High order numerical schemes for solving fractional powers of elliptic operators. Zbl 1440.65085
Čiegis, Raimondas; Vabishchevich, Petr N.
2020
Vector domain decomposition schemes for parabolic equations. Zbl 1454.65110
Vabishchevich, P. N.
2017
Iterative computational identification of a space-wise dependent source in parabolic equation. Zbl 1369.65118
Vabishchevich, P. N.
2017
Explicit-implicit schemes for first-order evolution equations. Zbl 1447.65031
Vabishchevich, P. N.
2020
Splitting schemes for pseudoparabolic equations. Zbl 1282.65104
Vabishchevich, P. N.; Grigor’ev, A. V.
2013
Two-level schemes of Cauchy problem method for solving fractional powers of elliptic operators. Zbl 1446.65062
Čiegis, Raimondas; Vabishchevich, Petr N.
2020
Approximation of a fractional power of an elliptic operator. Zbl 07217193
Vabishchevich, P. N.
2020
High order numerical schemes for solving fractional powers of elliptic operators. Zbl 1440.65085
Čiegis, Raimondas; Vabishchevich, Petr N.
2020
Explicit-implicit schemes for first-order evolution equations. Zbl 1447.65031
Vabishchevich, P. N.
2020
Computational identification of adsorption and desorption parameters for pore scale transport in periodic porous media. Zbl 1430.76441
Grigoriev, Vasiliy V.; Iliev, Oleg; Vabishchevich, Petr N.
2020
Three-level schemes for the advection equation. Zbl 1427.65188
Vabishchevich, P. N.
2019
Computational identification of the time dependence of the right-hand side of a hyperbolic equation. Zbl 1433.65199
Vabishchevich, P. N.
2019
Identification of the right-hand side of an equation with a fractional power of an elliptic operator. Zbl 07062831
Vabishchevich, Petr N.
2019
Numerical solution of time-dependent problems with fractional power elliptic operator. Zbl 1383.65128
Vabishchevich, Petr N.
2018
Minev, Peter; Vabishchevich, Petr N.
2018
Two-level schemes for the advection equation. Zbl 1392.76032
Vabishchevich, Petr N.
2018
Flux formulation of parabolic equations with highly heterogeneous coefficients. Zbl 1432.65132
Minev, Peter; Srinivasan, Shriram; Vabishchevich, Petr N.
2018
Numerical simulation of oxidation processes in a cross-flow around tube bundles. Zbl 07167908
Churbanov, Alexander G.; Iliev, Oleg; Strizhov, Valery F.; Vabishchevich, Petr N.
2018
Numerical solution of time-dependent problems with a fractional-power elliptic operator. Zbl 1457.65136
Vabishchevich, P. N.
2018
Two classes of vector domain decomposition schemes for time-dependent problems with overlapping subdomains. Zbl 07222745
Vabishchevich, Petr N.
2018
A numerical study of the homogeneous elliptic equation with fractional boundary conditions. Zbl 1364.65253
Lazarov, Raytcho; Vabishchevich, Petr
2017
Splitting schemes with respect to physical processes for double-porosity poroelasticity problems. Zbl 1457.76100
Kolesov, Alexander E.; Vabishchevich, Petr N.
2017
Vector domain decomposition schemes for parabolic equations. Zbl 1454.65110
Vabishchevich, P. N.
2017
Iterative computational identification of a space-wise dependent source in parabolic equation. Zbl 1369.65118
Vabishchevich, P. N.
2017
Preface: Numerical analysis of fractional differential equations. Zbl 1431.00030
Jin, Bangti; Lazarov, Raytcho; Vabishchevich, Petr
2017
Numerical solution of nonstationary problems for a space-fractional diffusion equation. Zbl 1382.65330
Vabishchevich, Petr N.
2016
Numerical identification of the leading coefficient of a parabolic equation. Zbl 1351.35087
Vabishchevich, P. N.; Klibanov, M. V.
2016
Numerical investigation of a space-fractional model of turbulent fluid flow in rectangular ducts. Zbl 1349.76444
Churbanov, Alexander G.; Vabishchevich, Petr N.
2016
Numerical solution of nonstationary problems for a convection and a space-fractional diffusion equation. Zbl 1348.65119
Vabishchevich, Petr
2016
A splitting scheme to solve an equation for fractional powers of elliptic operators. Zbl 1382.65358
Vabishchevich, Petr N.
2016
Alternating triangular schemes for convection-diffusion problems. Zbl 1457.65062
Vabishchevich, P. N.; Zakharov, P. E.
2016
An operator-splitting scheme for the stream function-vorticity formulation of the unsteady Navier-Stokes equations. Zbl 1326.35245
Minev, Peter; Vabishchevich, Petr N.
2016
Numerically solving an equation for fractional powers of elliptic operators. Zbl 1352.65557
Vabishchevich, Petr N.
2015
Computational identification of the right-hand side of a parabolic equation. Zbl 1325.65136
Vabishchevich, P. N.; Vasil&rsquo;ev, V. I.; Vasil&rsquo;eva, M. V.
2015
Explicit schemes for parabolic and hyperbolic equations. Zbl 1328.65185
Vabishchevich, P. N.
2015
Time step for numerically solving parabolic problems. Zbl 1359.65131
Vabishchevich, Petr N.
2015
Explicit-implicit splitting schemes for parabolic equations and systems. Zbl 1360.65219
Vabishchevich, Petr N.; Zakharov, Petr E.
2015
Splitting scheme for poroelasticity and thermoelasticity problems. Zbl 1426.74314
Kolesov, Alexandr E.; Vabishchevich, Petr N.; Vasilyeva, Maria V.; Gornov, Victor F.
2015
Computational algorithm for identification of the right-hand side of the parabolic equation. Zbl 1359.65184
Vabishchevich, Petr N.; Vasilyeva, Maria V.; Vasilyev, Vasily I.
2015
Additive operator-difference schemes. Splitting schemes. Zbl 1286.65105
Vabishchevich, Petr N.
2014
Splitting schemes for poroelasticity and thermoelasticity problems. Zbl 1368.74062
Kolesov, A. E.; Vabishchevich, P. N.; Vasilyeva, M. V.
2014
Explicit-implicit splitting schemes for some systems of evolutionary equations. Zbl 1310.65092
Gaspar, Francisco; Grigoriev, Alexander; Vabishchevich, Petr
2014
Computational determination of the lowest order coefficient in a parabolic equation. Zbl 1301.65103
Vabishchevich, P. N.; Vasil&rsquo;ev, V. I.
2014
Three-level schemes of the alternating triangular method. Zbl 1313.35175
Vabishchevich, P. N.
2014
Splitting scheme for poroelasticity and thermoelasticity problems. Zbl 1313.74033
Vabishchevich, P. N.; Vasil&rsquo;eva, M. V.; Kolesov, A. E.
2014
Additive schemes (splitting schemes) for some systems of evolutionary equations. Zbl 1297.65099
Vabishchevich, Petr N.
2014
Numerical modeling of thermal stabilization of filter ground. Zbl 1324.76077
Vabishchevich, P. N.; Vasilyeva, M. V.; Pavlova, N. V.
2014
Numerically solving the identification problem for the lower coefficient of a parabolic equation. Zbl 1374.65159
Vabishchevich, P. N.; Vasil&rsquo;ev, V. I.
2014
Mathematical modeling of the artificial freezing of soils. Zbl 1382.74128
Vabishchevich, Peter N.; Vasil&rsquo;eva, Mariya V.; Gornov, Viktor F.; Pavlova, Nataliya V.
2014
Unconditionally monotone schemes for unsteady convection-diffusion problems. Zbl 1393.65006
Afanas&rsquo;eva, Nadyezhda M.; Churbanov, Alexander G.; Vabishchevich, Petr N.
2013
Flux-splitting schemes for parabolic equations with mixed derivatives. Zbl 1299.35147
Vabishchevich, P. N.
2013
Unconditionally stable schemes for convection-diffusion problems. Zbl 1268.76040
Afanas&rsquo;eva, N. M.; Vabishchevich, P. N.; Vasil&rsquo;eva, M. V.
2013
Splitting schemes for hyperbolic heat conduction equation. Zbl 1278.65128
Vabishchevich, Petr N.
2013
Splitting schemes for pseudoparabolic equations. Zbl 1282.65104
Vabishchevich, P. N.; Grigor&rsquo;ev, A. V.
2013
Domain decomposition scheme for first-order evolution equations with nonselfadjoint operators. Zbl 1275.65032
Vabishchevich, Petr; Zakharov, Petr
2013
On a new class of additive (splitting) operator-difference schemes. Zbl 1251.65125
Vabishchevich, Petr N.
2012
Flux-splitting schemes for parabolic problems. Zbl 1274.35160
Vabishchevich, P. N.
2012
Finite difference analysis of a double-porosity consolidation model. Zbl 1373.76157
Boal, N.; Gaspar, F. J.; Lisbona, F. J.; Vabishchevich, P. N.
2012
Finite-difference analysis for the linear thermoporoelasticity problem and its numerical resolution by multigrid methods. Zbl 1238.74012
Boal, Natalia; Gaspar, Francisco José; Lisbona, Francisco; Vabishchevich, Petr
2012
SM-stability of operator-difference schemes. Zbl 1274.65260
Vabishchevich, P. N.
2012
Explicit-implicit schemes for convection-diffusion-reaction problems. Zbl 1299.65198
Vabishchevich, P. N.; Vasil&rsquo;eva, M. V.
2012
Iterative solution of the pressure problem for the multiphase filtration. Zbl 1323.76113
Vabishchevich, Petr; Vasil&rsquo;eva, Maria
2012
Domain decomposition schemes for the Stokes equation. Zbl 1265.76018
Vabishchevich, Petr N.
2012
Construction of splitting schemes based on transition operator approximation. Zbl 1249.65150
Vabishchevich, P. N.
2012
A substructuring domain decomposition scheme for unsteady problems. Zbl 1283.65095
Vabishchevich, Petr
2011
Finite-difference analysis of fully dynamic problems for saturated porous media. Zbl 1375.76106
Boal, N.; Gaspar, F. J.; Lisbona, F. J.; Vabishchevich, P. N.
2011
SM stability for time-dependent problems. Zbl 1317.65180
Vabishchevich, Petr N.
2011
Regularized additive operator-difference schemes. Zbl 1224.65213
Vabishchevich, P. N.
2010
Two-level finite difference scheme of improved accuracy order for time-dependent problems of mathematical physics. Zbl 1224.65184
Vabishchevich, P. N.
2010
Additive schemes for certain operator-differential equations. Zbl 1224.35328
Vabishchevich, P. N.
2010
Factorized SM-stable two-level schemes. Zbl 1224.65240
Vabishchevich, P. N.
2010
VAGO method for the solution of elliptic second-order boundary value problems. Zbl 1216.65144
Vabishchevich, N.; Vabishchevich, P.
2010
Domain decomposition methods with overlapping subdomains for the time-dependent problems of mathematical physics. Zbl 1156.65084
Vabishchevich, P. N.
2008
A stabilized method for a secondary consolidation Biot’s model. Zbl 1128.76043
Gaspar, F. J.; Gracia, J. L.; Lisbona, F. J.; Vabishchevich, P. N.
2008
Numerical methods for solving inverse problems of mathematical physics. Zbl 1136.65105
Samarskii, Alexander A.; Vabishchevich, Peter N.
2007
An efficient multigrid solver for a reformulated version of the poroelasticity system. Zbl 1173.74460
Gaspar, F. J.; Lisbona, F. J.; Oosterlee, C. W.; Vabishchevich, P. N.
2007
Reconstruction of the right-hand side of the elliptical equation from observation data obtained at the boundary. Zbl 1199.65373
Vabishchevich, Petr N.
2007
Staggered grid discretizations for the quasi-static Biot’s consolidation problem. Zbl 1091.76047
Gaspar, F. J.; Lisbona, F. J.; Vabishchevich, P. N.
2006
Stability of solutions of differential-operator and operator-difference equations in the sense of perturbation of operators. Zbl 1119.34046
Jovanović, B. S.; Lemeshevsky, S. V.; Matus, P. P.; Vabishchevich, P. N.
2006
Finite-difference approximation of mathematical physics problems on irregular grids. Zbl 1118.65377
Vabishchevich, P. N.
2005
On numerical solution of 1D poroelasticity equations in a multilayered domain. Zbl 1083.74051
Naumovich, A.; Iliev, O.; Gaspar, F.; Lisbona, F.; Vabishchevich, P.
2005
Difference schemes for nonstationary vector problems. Zbl 1105.78016
Vabishchevich, P. N.
2004
A finite difference analysis of Biot’s consolidation model. Zbl 1023.76032
Gaspar, F. J.; Lisbona, F. J.; Vabishchevich, P. N.
2003
Additive schemes for systems of time-dependent equations of mathematical physics. Zbl 1032.65097
Samarskii, Alexander; Vabishchevich, Petr
2003
Numerical solution of problems of identification of the right-hand side of a parabolic equation. Zbl 1074.65111
Vabishchevich, P. N.
2003
Difference schemes with operator factors. Zbl 1018.65103
Samarskii, A. A.; Matus, P. P.; Vabishchevich, P. N.
2002
Monotone finite-difference schemes on triangular grids for convection-diffusion problems. Zbl 1116.80304
Vabishchevich, P. N.; Samarskii, A. A.
2002
Finite difference schemes for poro-elastic problems. Zbl 1075.76600
Gaspar, F. J.; Lisbona, F. J.; Vabishchevich, P. N.
2002
Iterative methods for solving convection-diffusion problem. Zbl 1030.65106
Vabishchevich, P. N.
2002
Operator-splitting schemes for solving elasticity problems. Zbl 1054.65096
Lisbona, F. J.; Vabishchevich, P. N.
2001
Difference schemes for the transport equation. Zbl 1094.65082
Samarskii, A. A.; Vabishchevich, P. N.
2001
Stability of three-layer difference schemes on grids that are nonuniform with respect to time. Zbl 1046.65077
Samarskij, A. A.; Vabishchevich, P. N.; Makarevich, E. L.; Matus, P. P.
2001
Difference methods for solving problems of mathematical physics on unstructured grids. Zbl 1091.65505
Samarskiĭ, A. A.; Vabishchevich, P. N.
2001
Difference schemes for problems of filtration consolidation. Zbl 1090.65541
Samarskiĭ, A. A.; Vabishchevich, P. N.; Lisbona, F.
2001
Numerical solution of the inverse problem of reconstructing a distributed right-hand side of a parabolic equation. Zbl 0966.65067
Borukhov, V. T.; Vabishchevich, P. N.
2000
Difference methods for solving mathematical physics problems on unstructured grids. Zbl 1090.65540
Samarskii, A. A.; Vabishchevich, P. N.
2000
Finite difference schemes for convection-diffusion problems on irregular meshes. Zbl 0993.76058
Vabishchevich, P. N.; Samarskij, A. A.
2000
Problems in compressible fluid dynamics with a variable viscosity. Zbl 0998.76065
Vabishchevich, P. N.; Samarskij, A. A.
2000
Interpolation finite difference schemes on grids locally refined in time. Zbl 0978.65078
Shishkin, G. I.; Vabishchevich, P. N.
2000
Difference scheme of the second order of accuracy for Dirichlet problem in arbitrary domain. Zbl 1063.65575
Samarskij, A. A.; Vabishchevich, P. N.; Zyl&rsquo;, A. N.; Matus, P. P.
1999
Finite difference methods: theory and applications. Proceedings of the 1st conference on finite difference methods held in Rousse, Bulgaria, August 10–13, 1997. Zbl 0954.00042
Samarskiĭ, A. A.; Vabishchevich, Petr N.; Vulkov, Lubin G.
1999
Explicit-implicit difference schemes for convection-diffusion problems. Zbl 0980.65087
Samarskij, A. A.; Vabishchevich, P. N.
1999
Coefficient stability of operator-differential equations and operator-difference schemes. Zbl 1189.34107
Samarskiĭ, A. A.; Vabishchevich, P. N.; Matus, P. P.
1998
Regularized additive full approximation schemes. Zbl 0959.65099
Samarskij, A. A.; Vabishchevich, P. N.
1998
Vector additive schemes for second-order evolution equations. Zbl 0951.65081
Abrashin, V. N.; Vabishchevich, P. N.
1998
...and 56 more Documents
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#### Cited by 563 Authors

 75 Vabishchevich, Pëtr Nikolaevich 20 Gaspar, Francisco José 14 Matus, Pëtr Paŭlavich 11 Vasil’ev, Vasiliĭ Ivanovich 10 Rodrigo, Carmen 9 Lisbona Cortés, Francisco Javier 8 Arrarás, Andres 8 Minev, Peter Dimitrov 8 Portero, Laura 8 Vasilyeva, Maria V. 8 Vulkov, Lubin G. 7 Lazarov, Raytcho D. 6 Ashyralyev, Allaberen 6 Čiegis, Raimondas 6 Erdogan, Abdullah Said 6 Hieu, Le Minh 6 Hu, Xiaozhe 6 Kolesov, Aleksandr Egorovich 5 Ashyralyyev, Charyyar 5 Harizanov, Stanislav 5 Jorge, Juan Carlos 5 Kardashevsky, Anatoly Mikhailovich 5 Margenov, Svetozar D. 5 Oosterlee, Cornelis Willebrordus 5 Protsakh, Nataliya P. 5 Vasil’eva, Mariya V. 5 Zikatanov, Ludmil T. 4 Calo, Victor Manuel 4 Chung, Tsz Shun Eric 4 Iliev, Oleg P. 4 Liu, Chein-Shan 4 Srinivasan, Shriram 4 Wheeler, Mary Fanett 4 Yang, Danping 3 Adibi, Hojatollah 3 Ai, Zhiyong 3 Aida-Zade, Kamil Rajab 3 Brown, Donald L. 3 Cho, Chien-Hong 3 Dehghan Takht Fooladi, Mehdi 3 Deng, Quanling 3 Deng, Zuicha 3 Efendiev, Yalchin R. 3 Gavrilyuk, Ivan P. 3 Georgiev, Slavi G. 3 Gracia, José Luis 3 Hong, Qingguo 3 Kosturski, Nikola 3 Kraus, Johannes K. 3 Liang, Dong 3 Makarov, Volodymyr Leonidovych 3 Rashedi, Kamal 3 Vutov, Yavor 3 Yang, Liu 3 Zhou, Zhongguo 2 Abdullayev, Vaqif M. 2 Aceto, Lidia 2 Adler, James H. 2 Afanas’eva, Nadyezhda M. 2 Albu, Alla F. 2 Almani, Tameem 2 Behnoudfar, Pouria 2 Boal, Natalia 2 Botti, Michele 2 Cai, Xiao-Chuan 2 Chen, Jixin 2 Chen, Luoping 2 Chernysh, R. I. 2 Churbanov, Alexander G. 2 Dedeturk, Mutlu 2 Deng, Xiaomao 2 Di Pietro, Daniele Antonio 2 Đinh Nho Hào 2 Doroshenko, A. E. 2 Erkovan, Sait 2 Grigor’ev, A. V. 2 Grigoriev, Vasiliy V. 2 Hofreither, Clemens 2 Huong, Bui Viet 2 Hyman, Jeffrey D. 2 Ismailov, Mansur I. 2 Izsák, Ferenc 2 Jovanović, Boško S. 2 Karniadakis, George Em 2 Karra, Satish 2 Kokurin, Mikhail Mikhailovich 2 Koleva, Miglena N. 2 Kolodziej, Jan Adam 2 Kumar, Kundan 2 Kurganov, Alexander 2 Laevskiĭ, Yuriĭ Mironovich 2 Lapinska-Chrzczonowicz, Magdalena 2 Lazarev, Nyurgun Petrovich 2 Lemeshevskiǐ, S. V. 2 Luo, Guanwei 2 Luo, Peiyao 2 Lymbery, Maria 2 Makarov, Mikhail M. 2 Maros, Gábor 2 Mierzwiczak, Magdalena ...and 463 more Authors
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#### Cited in 111 Serials

 32 Journal of Computational and Applied Mathematics 27 Computers & Mathematics with Applications 26 Computational Mathematics and Mathematical Physics 22 Journal of Computational Physics 13 Computer Methods in Applied Mechanics and Engineering 12 Differential Equations 11 Applied Mathematics and Computation 11 Applied Numerical Mathematics 8 Fractional Calculus & Applied Analysis 7 Computational Methods in Applied Mathematics 6 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 6 Cybernetics and Systems Analysis 6 Journal of Mathematical Sciences (New York) 6 Computational and Applied Mathematics 6 Inverse Problems in Science and Engineering 5 International Journal of Heat and Mass Transfer 5 Mathematics and Computers in Simulation 5 Numerical Methods for Partial Differential Equations 5 Applied Mathematical Modelling 4 Computers and Fluids 4 Mathematics of Computation 4 Numerische Mathematik 4 International Journal of Numerical Methods for Heat & Fluid Flow 4 Journal of Inverse and Ill-Posed Problems 4 Computational Geosciences 4 Mathematical Modelling and Analysis 3 Ukrainian Mathematical Journal 3 Journal of Scientific Computing 3 Computational Mathematics and Modeling 3 Numerical Algorithms 3 Russian Mathematics 3 Doklady Mathematics 3 Abstract and Applied Analysis 3 Sibirskiĭ Zhurnal Industrial’noĭ Matematiki 3 Matematicheskoe Modelirovanie 3 Boundary Value Problems 2 Fluid Dynamics 2 International Journal for Numerical Methods in Engineering 2 Japan Journal of Industrial and Applied Mathematics 2 International Journal of Computer Mathematics 2 Stochastic Processes and their Applications 2 SIAM Journal on Scientific Computing 2 Electronic Journal of Differential Equations (EJDE) 2 Numerical Linear Algebra with Applications 2 Filomat 2 Russian Journal of Numerical Analysis and Mathematical Modelling 2 Engineering Analysis with Boundary Elements 2 Journal of Applied Mechanics and Technical Physics 2 Communications in Nonlinear Science and Numerical Simulation 2 Lobachevskii Journal of Mathematics 2 Nonlinear Analysis. Real World Applications 2 Journal of Numerical Mathematics 2 Multiscale Modeling & Simulation 2 Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki 2 Advances in Applied Mathematics and Mechanics 2 Open Mathematics 1 Acta Mechanica 1 Archive for Rational Mechanics and Analysis 1 Computer Physics Communications 1 Inverse Problems 1 Journal d’Analyse Mathématique 1 Journal of Fluid Mechanics 1 Journal of Mathematical Analysis and Applications 1 Lithuanian Mathematical Journal 1 Mathematical Methods in the Applied Sciences 1 Mathematical Notes 1 Moscow University Mathematics Bulletin 1 Acta Mathematica Vietnamica 1 BIT 1 Demonstratio Mathematica 1 Journal of Approximation Theory 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 SIAM Journal on Numerical Analysis 1 Siberian Mathematical Journal 1 Moscow University Computational Mathematics and Cybernetics 1 Chinese Annals of Mathematics. Series B 1 Acta Mathematicae Applicatae Sinica. English Series 1 Computational Mechanics 1 Journal of Applied Mathematics and Stochastic Analysis 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Vestnik St. Petersburg University. Mathematics 1 Physics of Fluids 1 Annales Mathématiques Blaise Pascal 1 ETNA. Electronic Transactions on Numerical Analysis 1 Advances in Computational Mathematics 1 Matematychni Metody ta Fizyko-Mekhanichni Polya 1 Mathematics and Mechanics of Solids 1 Computing and Visualization in Science 1 Matematychni Studiï 1 Discrete and Continuous Dynamical Systems. Series B 1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 1 Central European Journal of Mathematics 1 Hacettepe Journal of Mathematics and Statistics 1 Acta Numerica 1 Advances in Difference Equations 1 Sibirskie Èlektronnye Matematicheskie Izvestiya 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Annales Universitatis Mariae Curie-Skłodowska. Sectio A1. Informatica 1 Inverse Problems and Imaging 1 Mathematical Modelling of Natural Phenomena ...and 11 more Serials
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#### Cited in 29 Fields

 288 Numerical analysis (65-XX) 207 Partial differential equations (35-XX) 105 Fluid mechanics (76-XX) 52 Mechanics of deformable solids (74-XX) 26 Classical thermodynamics, heat transfer (80-XX) 13 Geophysics (86-XX) 12 Real functions (26-XX) 11 Calculus of variations and optimal control; optimization (49-XX) 10 Operator theory (47-XX) 8 Ordinary differential equations (34-XX) 8 Biology and other natural sciences (92-XX) 6 Optics, electromagnetic theory (78-XX) 5 Approximations and expansions (41-XX) 5 Computer science (68-XX) 5 Statistical mechanics, structure of matter (82-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Systems theory; control (93-XX) 4 Difference and functional equations (39-XX) 4 Integral equations (45-XX) 4 Probability theory and stochastic processes (60-XX) 3 Operations research, mathematical programming (90-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 1 General and overarching topics; collections (00-XX) 1 Integral transforms, operational calculus (44-XX) 1 Functional analysis (46-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Statistics (62-XX) 1 Relativity and gravitational theory (83-XX) 1 Information and communication theory, circuits (94-XX)