相关论文: Domain decomposition schemes for evolutionary equa…
Domain decomposition methods are used for approximate solving boundary problems for partial differential equations on parallel computing systems. Specific features of unsteady problems are taken into account in the most complete way in…
Stable computational algorithms for the approximate solution of the Cauchy problem for nonstationary problems are based on implicit time approximations. Computational costs for boundary value problems for systems of coupled multidimensional…
We consider the Cauchy problem for a second-order evolution equation, in which the problem operator is the sum of two self-adjoint operators. The main feature of the problem is that one of the operators is represented in the form of the…
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 easily constructed and relatively uncomplicated to investigate…
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…
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…
An iteration-free method of domain decomposition is considered for approximate solving a boundary value problem for a second-order parabolic equation. A standard approach to constructing domain decomposition schemes is based on a partition…
On the basis of additive schemes (splitting schemes) we construct efficient numerical algorithms to solve approximately the initial-boundary value problems for systems of time-dependent partial differential equations (PDEs). In many applied…
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…
Numerical algorithms for solving problems of mathematical physics on modern parallel computers employ various domain decomposition techniques. Domain decomposition schemes are developed here to solve numerically initial/boundary value…
In approximating solutions of nonstationary problems, various approaches are used to compute the solution at a new time level from a number of simpler (sub-)problems. Among these approaches are splitting methods. Standard splitting schemes…
In recent years, SPDEs have become a well-studied field in mathematics. With their increase in popularity, it becomes important to efficiently approximate their solutions. Thus, our goal is a contribution towards the development of…
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. The implicit two-level scheme based on the Pad\'{e}…
Many applied time-dependent problems are characterized by an additive representation of the problem operator. Additive schemes are constructed using such a splitting and associated with the transition to a new time level on the basis of the…
Domain decomposition (DD) methods for solving time-dependent problems can be classified by (i) the method of domain decomposition used, (ii) the choice of decomposition operators (exchange of boundary conditions), and (iii) the splitting…
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 second order. Finite element approximation in space is employed.…
We analyze temporal approximation schemes based on overlapping domain decompositions. As such schemes enable computations on parallel and distributed hardware, they are commonly used when integrating large-scale parabolic systems. Our…
As is known, the problems for the differential equations with continuously changing order of the derivatives are not considered completely. In this paper we consider the initial and boundary value problems for this type of linear ordinary…
Problems of the numerical solution of the Cauchy problem for a first-order differential-operator equation are discussed. A fundamental feature of the problem under study is that the equation includes a fractional power of the self-adjoint…
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 employed. The proposed numerical algorithm is based on solving an…