Zobrazeno 1 - 10
of 227
pro vyhledávání: '"Vabishchevich, Petr N."'
Autor:
Vabishchevich, Petr N.
Formulating boundary value problems for multidimensional partial derivative equations in terms of invariant operators of vector (tensor) analysis is convenient. Computational algorithms for approximate solutions are based on constructing grid analogs
Externí odkaz:
http://arxiv.org/abs/2409.16151
Autor:
Vabishchevich, Petr N.
Numerical methods of approximate solution of the Cauchy problem for coupled systems of evolution equations are considered. Separating simpler subproblems for individual components of the solution achieves simplification of the problem at a new level
Externí odkaz:
http://arxiv.org/abs/2408.13553
Autor:
Vabishchevich, Petr N.
In computational practice, most attention is paid to rational approximations of functions and approximations by the sum of exponents. We consider a wide enough class of nonlinear approximations characterized by a set of two required parameters. The a
Externí odkaz:
http://arxiv.org/abs/2301.05881
Autor:
Vabishchevich, Petr N.
The reduction of computational costs in the numerical solution of nonstationary problems is achieved through splitting schemes. In this case, solving a set of less computationally complex problems provides the transition to a new level in time. The t
Externí odkaz:
http://arxiv.org/abs/2206.12143
In this paper, we consider a class of convection-diffusion equations with memory effects. These equations arise as a result of homogenization or upscaling of linear transport equations in heterogeneous media and play an important role in many applica
Externí odkaz:
http://arxiv.org/abs/2204.00554
Autor:
Vabishchevich, Petr N.
It is necessary to use more general models than the classical Fourier heat conduction law to describe small-scale thermal conductivity processes. The effects of heat flow memory and heat capacity memory (internal energy) in solids are considered in f
Externí odkaz:
http://arxiv.org/abs/2111.14090
Autor:
Vabishchevich, Petr N.
We consider the Cauchy problem for a first-order evolution equation with memory in a finite-dimensional Hilbert space when the integral term is related to the time derivative of the solution. The main problems of the approximate solution of such nonl
Externí odkaz:
http://arxiv.org/abs/2111.05121
Autor:
Vabishchevich, Petr N.
We consider the problems of the numerical solution of the Cauchy problem for an evolutionary equation with memory when the kernel of the integral term is a difference one. The computational implementation is associated with the need to work with an a
Externí odkaz:
http://arxiv.org/abs/2110.15125
Autor:
Vabishchevich, Petr N.
Several applied problems are characterized by the need to numerically solve equations with an operator function (matrix function). In particular, in the last decade, mathematical models with a fractional power of an elliptic operator and numerical me
Externí odkaz:
http://arxiv.org/abs/2105.10432
In this work, we design and investigate contrast-independent partially explicit time discretizations for wave equations in heterogeneous high-contrast media. We consider multiscale problems, where the spatial heterogeneities are at subgrid level and
Externí odkaz:
http://arxiv.org/abs/2102.13198