相关论文: Canards in modified equations for Euler discretiza…
Several quantum gravity approaches and field theory on an evolving lattice involve a discretization changing dynamics generated by evolution moves. Local evolution moves in variational discrete systems (1) are a generalization of the…
We prove stability and convergence of a full discretization for a class of stochastic evolution equations with super-linearly growing operators appearing in the drift term. This is done using the recently developed tamed Euler method, which…
We present an algorithm that takes as input a finite point set in Euclidean space, and performs a perturbation that guarantees that the Delaunay triangulation of the resulting perturbed point set has quantifiable stability with respect to…
We study a discrete variant of the Airy equation, formulated as an advance-delay equation, to reveal that discretization induces the higher-order Stokes phenomenon, which is not present in the continuous Airy function and is typically only…
The Reynolds equation, combined with the Elrod algorithm for including the effect of cavitation, resembles a nonlinear convection-diffusion-reaction (CDR) equation. Its solution by finite elements is prone to oscillations in…
In this paper we investigate a variational discretization for the class of mechanical systems in presence of symmetries described by the action of a Lie group which reduces the phase space to a (non-trivial) principal bundle. By introducing…
By applying a singular perturbation approach, canard limit cycles exhibited by a general family of singularly perturbed planar piecewise linear (PWL) differential systems are analyzed. The performed study involves both hyperbolic and…
The problem of precise evaluation of perturbative QCD predictions at moderate energies is addressed. In order to improve stability of the predictions with respect to change of the renormalization scheme it is proposed to replace the…
The two-fold singularity has played a significant role in our understanding of uniqueness and stability in piecewise smooth dynamical systems. When a vector field is discontinuous at some hypersurface, it can become tangent to that surface…
We compare the performance of several discretizations of the simple pendulum equation in a series of numerical experiments. The stress is put on the long-time behaviour. We choose for the comparison numerical schemes which preserve the…
Viewing optimization methods as numerical integrators for ordinary differential equations (ODEs) provides a thought-provoking modern framework for studying accelerated first-order optimizers. In this literature, acceleration is often…
In this paper, a backward Euler method combined with finite element discretization in spatial direction is discussed for the equations of motion arising in the $2D$ Oldroyd model of viscoelastic fluids of order one with the forcing term…
We study the quantum dynamics generated by the repeated action of a non-unitary evolution operator on a system of qubits. Breaking unitarity can lead to the purification of mixed initial states, which corresponds to the loss of sensitivity…
By developing new efficient techniques and using an appropriate fixed point theorem, we derive several new sufficient conditions for the pseudo almost periodic solutions with double measure for some system of differential equations with…
Semidiscretization in time is studied for a class of quasi-linear evolution equations in a framework due to Kato, which applies to symmetric first-order hyperbolic systems and to a variety of fluid and wave equations. In the regime where…
We show that there exist generic slow-fast systems with only one (time-scaling) parameter on the two-torus, which have canard cycles for arbitrary small values of this parameter. This is in drastic contrast with the planar case, where…
As a first step towards the numerical analysis of the stochastic primitive equations of the atmosphere and oceans, we study their time discretization by an implicit Euler scheme. From deterministic viewpoint the 3D Primitive Equations are…
In this paper we address the existence, uniqueness and approximation of solutions of delay differential equations (DDEs) with Carath\'eodory type right-hand side functions. We provide construction of randomized Euler scheme for DDEs and…
In this paper, we present a comprehensive long-time stability analysis of a second-order explicit exponential Runge--Kutta (ERK2) method for the Cahn--Hilliard (CH) equation. By employing Fourier spectral collocation in space and a…
In this paper we introduce a randomized version of the backward Euler method, that is applicable to stiff ordinary differential equations and nonlinear evolution equations with time-irregular coefficients. In the finite-dimensional case, we…