79 citations · 263 across the 55 of their papers we have counts for
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Two-level schemes for the advection equation
Petr N. Vabishchevich
The advection equation is the basis for mathematical models of continuum mechanics. In the approximate solution of nonstationary problems it is necessary to inherit main properties…
Numerical simulation of oxidation processes in a cross-flow around tube bundles
Alexander G. Churbanov, Oleg Iliev, Valery F. Strizhov +1
An oxidation process is simulated for a bundle of metal tubes in a cross-flow. A fluid flow is governed by the incompressible Navier-Stokes equations. To describe the transport of…
State change modal method for numerical simulation of dynamic processes in a nuclear reactor
Alexander V. Avvakumov, Valery F. Strizhov, Petr N. Vabishchevich +1
Modeling of dynamic processes in nuclear reactors is carried out, mainly, on the basis of the multigroup diffusion approximation for the neutron flux. The basic model includes a mu…
Fundamental mode exact schemes for unsteady problems
Petr N. Vabishchevich
The problem of increasing the accuracy of an approximate solution is considered for boundary value problems for parabolic equations. For ordinary differential equations (ODEs), non…
Two-component domain decomposition scheme with overlapping subdomains for parabolic equations
Petr N. Vabishchevich
An iteration-free method of domain decomposition is considered for approximate solving a boundary value problem for a second-order parabolic equation. A standard approach to constr…
Numerical solution of time-dependent problems with fractional power elliptic operator
Petr N. Vabishchevich
An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves a fractional power of an elliptic operator of se…
A numerical study of the homogeneous elliptic equation with fractional order boundary conditions
Raytcho Lazarov, Petr Vabishchevich
We consider the homogeneous equation , where is a symmetric and coercive elliptic operator in with bounded domain in .…