79 citations · 263 across the 55 of their papers we have counts for
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Splitting schemes for poroelasticity and thermoelasticity problems
A. E. Kolesov, P. N. Vabishchevich, M. V. Vasilyeva
In this work, we consider the coupled systems of linear unsteady partial differential equations, which arise in the modeling of poroelasticity processes. Stability estimates of wei…
A priori estimation of a time step for numerically solving parabolic problems
Petr N. Vabishchevich
This work deals with the problem of choosing a time step for the numerical solution of boundary value problems for parabolic equations. The problem solution is derived using the fu…
Explicit schemes for parabolic and hyperbolic equations
Petr N. Vabishchevich
Standard explicit schemes for parabolic equations are not very convenient for computing practice due to the fact that they have strong restrictions on a time step. More promising e…
Numerical solving the identification problem for the lower coefficient of parabolic equation
P. N. Vabishchevich, V. I. Vasil'ev
In the theory and practice of inverse problems for partial differential equations (PDEs) much attention is paid to the problem of the identification of coefficients from some addit…
Mathematical modeling of thermal stabilization of vertical wells on high performance computing systems
Natalia V. Pavlova, Petr N. Vabishchevich, Maria V. Vasilyeva
Temperature stabilization of oil and gas wells is used to ensure stability and prevent deformation of a subgrade estuary zone. In this work, we consider the numerical simulation of…