Search Results - "Vabishchevich, P. N"

Numerical Solution of the Cauchy Problem for a Second-Order Integro-Differential Equation by Vabishchevich, P. N.

“…In a finite-dimensional Hilbert space, we consider the Cauchy problem for a second-order integro-differential evolution equation with memory where the…”
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Solution Decomposition Schemes for Second-Order Evolution Equations by Vabishchevich, P. N.

“…For evolution problems, the approximate solution on the upper time level is often obtained from a number of simpler problems. Standard splitting schemes use an…”
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Approximation of a fractional power of an elliptic operator by Vabishchevich, P. N.

“…Summary Some mathematical models of applied problems lead to the need of solving boundary value problems with a fractional power of an elliptic operator. In a…”
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Difference Operator Approximations on Nonstandard Rectangular Grid by Vabishchevich, P. N.

“…Difference methods are widely used for the approximate solution of boundary value problems for partial differential equations. Grid approximations are most…”
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Three-Level Schemes with Double Change in the Time Step by Vabishchevich, P. N.

“…Nonstationary problems are solved numerically by applying multilevel (with more than two levels) time approximations. They are easy to construct and relatively…”
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Difference Decomposition Schemes Based on Splitting the Solution and Operator of the Problem by Vabishchevich, P. N.

“…Domain decomposition methods are used for the approximate solution of boundary value problems for partial differential equations on parallel computing systems…”
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Numerical-analytical Methods for Solving the Cauchy Problem for Evolutionary Equations with Memory by Vabishchevich, P. N.

“…Many applied problems lead to the necessity of solving boundary value problems for evolutionary integrodifferential equations of the first order. Such models…”
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Splitting Schemes with Additive Representation of the Operator at the Time Derivative by Vabishchevich, P. N.

“…Additive (splitting) schemes are used to contruct effective computational algorithms for approximately solving initial-boundary value problems for…”
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On Stability of an Approximate Solution of the Cauchy Problem for Some First-Order Integrodifferential Equations by Vabishchevich, P. N.

“…The Cauchy problem for a first-order evolutionary equation with memory with the time derivative of the Volterra integral term and difference kernel in the…”
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Splitting Schemes for One Class of Operator Differential Equations by Vabishchevich, P. N.

“…At present, splitting schemes of various types are available for evolution equations of the first and second order in the case when the basic elliptic operator…”
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Explicit–Implicit Schemes for First-Order Evolution Equations by Vabishchevich, P. N.

“…Computational practice widely employs inhomogeneous time approximations in which one part of the problem operator is taken from the lower time level and the…”
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Computational algorithms for solving the coefficient inverse problem for parabolic equations by Vabishchevich, P.N., Vasil'ev, V.I.

“…Among inverse problems for partial differential equations, we distinguish coefficient inverse problems, which are associated with the identification of…”
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Monotone Schemes for Convection–Diffusion Problems with Convective Transport in Different Forms by Vabishchevich, P. N.

“…Convective transport in convection–diffusion problems can be formulated differently. Convective terms are commonly written in nondivergent or divergent form…”
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Computational Identification of the Time Dependence of the Right-Hand Side of a Hyperbolic Equation by Vabishchevich, P. N.

“…Many applied problems lead to the necessity of solving inverse problems for partial differential equations. In particular, much attention is paid to the…”
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Iterative computational identification of a space-wise dependent source in parabolic equation by Vabishchevich, P. N.

“…Coefficient inverse problems related to identifying the right-hand side of an equation with use of additional information is of interest among inverse problems…”
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Numerical Solution of Time-Dependent Problems with a Fractional-Power Elliptic Operator by Vabishchevich, P. N.

“…A time-dependent problem in a bounded domain for a fractional diffusion equation is considered. The first-order evolution equation involves a fractional-power…”
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Alternating Triangular Schemes for Second-Order Evolution Equations by Vabishchevich, P. N.

“…Schemes of the Samarskii alternating triangular method are based on splitting the problem operator into two operators that are conjugate to each other. When…”
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Vector domain decomposition schemes for parabolic equations by Vabishchevich, P. N.

“…A new class of domain decomposition schemes for finding approximate solutions of timedependent problems for partial differential equations is proposed and…”
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Explicit schemes for parabolic and hyperbolic equations by Vabishchevich, P.N.

“…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…”
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Splitting schemes for poroelasticity and thermoelasticity problems by Kolesov, A.E., Vabishchevich, P.N., Vasilyeva, M.V.

“…In this work, we consider the coupled systems of linear unsteady partial differential equations, which arise in the modelling of poroelasticity processes…”
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