79 citations · 263 across the 55 of their papers we have counts for
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Numerical solving unsteady space-fractional problems with the square root of an 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 the square root of an elliptic operator of secon…
Numerical simulation of the stress-strain state of the dental system
Sergey V. Lemeshevsky, Semion A. Naumovich, Sergey S. Naumovich +2
We present mathematical models, computational algorithms and software, which can be used for prediction of results of prosthetic treatment. More interest issue is biomechanics of t…
A splitting scheme to solve an equation for fractional powers of elliptic operators
Petr N. Vabishchevich
An equation containing a fractional power of an elliptic operator of second order is studied for Dirichlet boundary conditions. Finite difference approximations in space are employ…
Numerical investigation of a space-fractional model of turbulent fluid flow in rectangular ducts
Alexander G. Churbanov, Petr N. Vabishchevich
The models that are based of fractional derivatives should be highlighted among promising new models to describe turbulent fluid flows. In the present work, a steady-state flow in…
Factorized schemes of second-order accuracy for numerical solving unsteady problems
P. N. Vabishchevich
Schemes with the second-order approximation in time are considered for numerical solving the Cauchy problem for an evolutionary equation of first order with a self-adjoint operator…