Related papers: Splitting Schemes for Some Second-Order Evolution …
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…
Domain decomposition methods are essential in solving applied problems on parallel computer systems. For boundary value problems for evolutionary equations the implicit schemes are in common use to solve problems at a new time level…
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}…
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…
In this paper, we define an operator function as a series of operators corresponding to the Taylor series representing the function of the complex variable. In previous papers, we considered the case when a function has a decomposition in…
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…
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…
We provide general product formulas for the solutions of non-autonomous abstract Cauchy problems. The main technical tool is the application of evolution semigroup methods, allowing the direct application of existing results on autonomous…
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 consider the Cauchy problem for a second-order nonlinear evolution equation in a Hilbert space. This equation represents the abstract generalization of the Ball integro-differential equation. The general nonlinear case with respect to…
Existence of strong solutions of an abstract Cauchy problem for a class of doubly nonlinear evolution inclusion of second order is established via a semi-implicit time discretization method. The principal parts of the operators acting on…
We consider solutions of the Cauchy problem for semilinear equations with (possibly) different L\'evy operators. We provide various results on their convergence under the assumption that symbols of the involved operators converge to the…
In this study, we analyze a semilinear damped evolution equation under different damping conditions, including the undamped $(\theta=0)$, effectively damped $(0<2\theta<\sigma)$, critically damped $(2\theta=\sigma)$, and non-effectively…
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…
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…
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 an evolution equation with the regularized fractional derivative of an order $\alpha \in (0,1)$ with respect to the time variable, and a uniformly elliptic operator with variable coefficients acting in the spatial variables.…
We investigate the following fractional order in time Cauchy problem \begin{equation*} \begin{cases} \mathbb{D}_{t}^{\alpha }u(t)+Au(t)=f(u(t)), & 1<\alpha <2, \\ u(0)=u_{0},\,\,\,u^{\prime }(0)=u_{1}. & \end{cases}% \end{equation*}% where…
We study Cauchy problems of fractional differential equations in both space and time variables by expressing the solution in terms of ``stochastic composition" of the solutions to two simpler problems. These Cauchy sub-problems respectively…
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…