Related papers: Semidiscrete variable time-step \theta-scheme for …
The Gross-Pitaevskii equation with a local cubic nonlinearity that describes a many-dimensional system in an external field is considered in the framework of the complex WKB-Maslov method. Analytic asymptotic solutions are constructed in…
In this work we begin a theoretical and numerical investigation on the spectra of evolution operators of neutral renewal equations, with the stability of equilibria and periodic orbits in mind. We start from the simplest form of linear…
In this paper we investigate a class of nonautonomous linear parabolic problems with time depending Ornstein-Uhlenbeck operators. We study the asymptotic behavior of the associated evolution operator and evolution semigroup in the periodic…
In this paper, we discuss the well-posedness of the Cauchy problem associated with the third-order evolution equation in time $$ u_{ttt} +A u + \eta A^{\frac13} u_{tt} +\eta A^{\frac23} u_t=f(u) $$ where $\eta>0$, $X$ is a separable Hilbert…
We consider a coupled Wave-Klein-Gordon system in 3D, which is a simplified model for the global nonlinear stability of the Minkowski space-time for self-gravitating massive fields. In this paper we study the large-time asymptotic behavior…
We construct a symplectic integrator for non-separable Hamiltonian systems combining an extended phase space approach of Pihajoki and the symmetric projection method. The resulting method is semiexplicit in the sense that the main time…
We investigate the geometric structure of adjoint systems associated with evolutionary partial differential equations at the fully continuous, semi-discrete, and fully discrete levels and the relations between these levels. We show that the…
In this note we present a framework which allows to prove an abstract existence result for evolution equations with pseudo-monotone operators. The assumptions on the spaces and the operators can be easily verified in concrete examples.
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…
This paper deals with the approximation of the spectrum of linear and nonautonomous delay differential equations through the reduction of the relevant evolution semigroup from infinite to finite dimension. The focus is placed on classic…
We study an abstract second order inclusion involving two nonlinear single-valued operators and a nonlinear multivalued term. Our goal is to establish the existence of solutions to the problem by applying numerical scheme based on time…
We propose consistent locally stabilized, conforming finite element schemes on completely unstructured simplicial space-time meshes for the numerical solution of non-autonomous parabolic evolution problems under the assumption of maximal…
In this paper we develop a new approach to stochastic evolution equations with an unbounded drift $A$ which is dependent on time and the underlying probability space in an adapted way. It is well-known that the semigroup approach to…
We deal with an initial-boundary value problem for the multidimensional acoustic wave equation, with the variable speed of sound. For a three-level semi-explicit in time higher-order vector compact scheme, we prove stability and derive 4th…
The method of multiscale analysis is constructed for dicrete systems of evolution equations for which the problem is that of the far behavior of an input boundary datum. Discrete slow space variables are introduced in a general setting and…
We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…
Active Flux is an extension of the Finite Volume method and additionally incorporates point values located at cell boundaries. This gives rise to a globally continuous approximation of the solution. Originally, the Active Flux method…
We consider a wide class of semi linear Hamiltonian partial differential equa- tions and their approximation by time splitting methods. We assume that the nonlinearity is polynomial, and that the numerical tra jectory remains at least uni-…
This paper deals with the application of probabilistic time integration methods to semi-explicit partial differential-algebraic equations of parabolic type and its semi-discrete counterparts, namely semi-explicit differential-algebraic…
New implicit and implicit-explicit time-stepping methods for the wave equation in second-order form are described with application to two and three-dimensional problems discretized on overset grids. The implicit schemes are single step,…