Related papers: Operator Splitting Methods for Numerical Solutions…
In this paper we describe an iterative operator-splitting method for unbounded operators. We derive error bounds for iterative splitting methods in the presence of unbounded operators and semigroup operators. Here mixed applications of…
Recent results of L. Zsido, based on his previous work with C. P. Niculescu and A. Stroh, on actions of topological semigroups on von Neumann algebras, give a Jacobs-de Leeuw-Glicksberg splitting theorem at the von Neumann algebra (rather…
Operator splitting is an effective technique for the numerical solution of nonlinear partial differential equations by decomposing a complex problem into simpler subproblems. In this study, we present and analyze a fully discrete scheme for…
Nonlinear ordinary differential equations can rarely be solved analytically. Koopman operator theory provides a way to solve nonlinear systems by mapping nonlinear dynamics to a linear space using eigenfunctions. Unfortunately, finding such…
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 investigate the equivalence of different operator-splitting schemes for the integration of the Langevin equation. We consider a specific problem, so called the directed percolation process, which can be extended to a wider class of…
We propose a new primal-dual splitting method for solving composite inclusions involving Lipschitzian, and parallel-sum-type monotone operators. Our approach extends the framework in \cite{Siopt4} to a more general class of monotone…
This article is devoted to the construction of new numerical methods for the semiclassical Schr\"odinger equation. A phase-amplitude reformulation of the equation is described where the Planck constant epsilon is not a singular parameter.…
Proper splittings of operators are commonly used to study the convergence of iterative processes. In order to approximate solutions of operator equations, in this article we deal with proper splittings of closed range bounded linear…
We define a class of discrete operators acting on infinite, finite or periodic sequences mimicking the standard properties of pseudo-differential operators. In particular we can define the notion of order and regularity, and we recover the…
This article explores an algebraic-recursive approach to construct differential operators that commute with a central operator $\hat{H}$ in quantum mechanics. Starting from the Schr\"odinger equation for a free particle, the work derives…
We consider Lie and Strang splitting for the time integration of constrained partial differential equations with a nonlinear reaction term. Since such systems are known to be sensitive with respect to perturbations, the splitting procedure…
The goal of this work is to develop a novel splitting approach for the numerical solution of multiscale problems involving the coupling between Stokes equations and ODE systems, as often encountered in blood flow modeling applications. The…
We study an operator analogue of the classical problem of finding the rate of decay of an oscillatory integral on the real line. This particular problem arose in the analysis of oscillatory Riemann-Hilbert problems associated with partial…
Recent advances in Schramm-Loewner evolution have driven increasing interest in non-standard Loewner flows. In this work, we propose a novel splitting algorithm to simulate random Loewner curves with rigorous convergence analysis in…
The explicit split-operator algorithm is often used for solving the linear and nonlinear time-dependent Schr\"{o}dinger equations. However, when applied to certain nonlinear time-dependent Schr\"{o}dinger equations, this algorithm loses…
Coupled multi-physics problems are encountered in countless applications and pose significant numerical challenges. Although monolithic approaches offer possibly the best solution strategy, they often require ad-hoc preconditioners and…
This work introduces a methodology for generating linear operators that approximately represent nonlinear systems of perturbed ordinary differential equations. This is done through the application of classical perturbation theory via the…
Many dimensionality and model reduction techniques rely on estimating dominant eigenfunctions of associated dynamical operators from data. Important examples include the Koopman operator and its generator, but also the Schr\"odinger…
The homogenization of elliptic divergence-type fourth-order operators with periodic coefficients is studied in a (periodic) domain. The aim is to find an operator with constant coefficients and represent the equation through a perturbation…