Related papers: Operator splittings and spatial approximations for…
In this work we study operator splitting methods for a certain class of coupled abstract Cauchy problems, where the coupling is such that one of the problems prescribes a "boundary type" extra condition for the other one. The theory of…
We propose a quasi-random operator splitting method for evolution equations driven by multiple mechanisms. The method uses a low-discrepancy sequence to generate the ordering of the subflows, while requiring only one application of each…
We provide a new analytical approach to operator splitting for equations of the type $u_t=Au+u u_x$ where $A$ is a linear differential operator such that the equation is well-posed. Particular examples include the viscous Burgers' equation,…
In this paper we study the convergence of a Lie-Trotter operator splitting for stochastic semi-linear evolution equations in a Hilbert space. The abstract Hilbert space setting allows for the consideration of convergence of the…
The error behavior of exponential operator splitting methods for nonlinear Schr{\"o}dinger equations in the semiclassical regime is studied. For the Lie and Strang splitting methods, the exact form of the local error is determined and the…
This survey describes the method of approximation of operator semigroups, based on the Chernoff theorem. We outline recent results in this domain as well as clarify relations between constructed approximations, stochastic processes,…
We introduce a new system of split variational inequality problems which is a natural extension of split variational inequality problem in semi-inner product spaces. We use the retraction technique to propose an iterative algorithm for…
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…
In this paper, we are concerned with a operator splitting scheme for linear fractional and fractional degenerate stochastic conservation laws driven by multiplicative Levy noise. More specifically, using a variant of classical Kruzkov's…
We present easy to verify conditions implying stability estimates for operator matrix splittings which ensure convergence of the associated Trotter, Strang and weighted product formulas. The results are applied to inhomogeneous abstract…
This work proposes and analyzes an efficient numerical method for solving the nonlinear Schr\"odinger equation with quasiperiodic potential, where the projection method is applied in space to account for the quasiperiodic structure and the…
Operator splitting methods allow to split the operator describing a complex dynamical system into a sequence of simpler subsystems and treat each part independently. In the modeling of dynamical problems, systems of (possibly coupled)…
Operator splitting is a popular divide-and-conquer strategy for solving differential equations. Typically, the right-hand side of the differential equation is split into a number of parts that are then integrated separately. Many methods…
In this paper, we propose a numerical scheme for structured population models defined on a separable and complete metric space. In particular, we consider a generalized version of a transport equation with additional growth and non-local…
This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady…
The Douglas--Rachford and Peaceman--Rachford splitting methods are common choices for temporal discretizations of evolution equations. In this paper we combine these methods with spatial discretizations fulfilling some easily verifiable…
An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves a fractional power of an elliptic operator of second order. Finite element approximation in space is…
We study operator-splitting schemes for approximating Koopman generators of linear semigroups induced by nonlinear flows, a framework originating with Dorroh and Neuberger. Building on ideas of Lie, Kowalewski, and Gr\"{o}bner, we analyze…
In [8], some exact splittings are proposed for inhomogeneous quadratic differential equations including, for example, transport equations, kinetic equations, and Schr{\"o}dinger type equations with a rotation term. In this work, these exact…
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…