79 citations · 263 across the 55 of their papers we have counts for
66 papers
Stability analysis of the steady solution for incompressible lid-driven cavity flow
Dmitri Lomasov, Petr Vabishchevich
Steady solutions at high Reynolds numbers are computed using an iterative method that linearizes the nonlinear convective terms. This linearization reduces the original nonlinear b…
Splitting schemes for problems with memory
Petr N. Vabishchevich
The paper considers the Cauchy problem for a first-order integro-differential equation with memory in a finite-dimensional Hilbert space. The main computational difficulty of such…
Operator-difference approximations on two-dimensional merged Voronoi-Delaunay grids
Petr N. Vabishchevich
Formulating boundary value problems for multidimensional partial derivative equations in terms of invariant operators of vector (tensor) analysis is convenient. Computational algor…
Decoupling technology for systems of evolutionary equations
Petr N. Vabishchevich
Numerical methods of approximate solution of the Cauchy problem for coupled systems of evolution equations are considered. Separating simpler subproblems for individual components…
Computational decomposition and composition technique for approximate solution of nonstationary problems
P. N. Vabishchevich
Stable computational algorithms for the approximate solution of the Cauchy problem for nonstationary problems are based on implicit time approximations. Computational costs for bou…
Operator-difference schemes on non-uniform grids for second-order evolutionary equations
P. N. Vabishchevich
The approximate solution of the Cauchy problem for second-order evolution equations is performed, first of all, using three-level time approximations. Such approximations are easil…