Related papers: A New Optimality Property of Strang's Splitting
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…
We consider a class of nonlinear non-diagonal elliptic systems with $p$-growth and establish the $L^q$-integrability for all $q\in [p,p+2]$ of any weak solution provided the corresponding right hand side belongs to the corresponding…
Operator-splitting methods are widely used to solve differential equations, especially those that arise from multi-scale or multi-physics models, because a monolithic (single-method) approach may be inefficient or even infeasible. The most…
In this paper we consider splitting methods for nonlinear ordinary differential equations in which one of the (partial) flows that results from the splitting procedure can not be computed exactly. Instead, we insert a well-chosen state…
Strang splitting is a well established tool for the numerical integration of evolution equations. It allows the application of tailored integrators for different parts of the vector field. However, it is also prone to order reduction in the…
We consider a class of second-order Strang splitting methods for Allen-Cahn equations with polynomial or logarithmic nonlinearities. For the polynomial case both the linear and the nonlinear propagators are computed explicitly. We show that…
In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow can not be computed exactly. Instead, we use a numerical…
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…
We propose and analyze a second-order Strang splitting method for a class of stiff matrix differential equations with Sylvester-type structure. The method splits the dynamics into a stiff linear part, treated exactly via matrix…
The implementation of multi-stage splitting integrators is essentially the same as the implementation of the familiar Strang/Verlet method. Therefore multi-stage formulas may be easily incorporated into software that now uses the…
We introduce three models of fragmentation in which the largest fragment in the system can be broken at each time step with a fixed probability, p. We solve these models exactly in the long time limit to reveal stable time invariant…
We study the Strang splitting scheme for quasilinear Schr\"odinger equations. We establish the convergence of the scheme for solutions with small initial data. We analyze the linear instability of the numerical scheme, which explains the…
Mesoscopic models in the reaction-diffusion framework have gained recognition as a viable approach to describing chemical processes in cell biology. The resulting computational problem is a continuous-time Markov chain on a discrete and…
We consider a Strang-type second order operator-splitting discretization for the Cahn-Hilliard equation. We introduce a new theoretical framework and prove uniform energy stability of the numerical solution and persistence of all higher…
We investigate the stability and stabilization concepts for infinite dimensional time fractional differential linear systems in Hilbert spaces with Caputo derivatives. Firstly, based on a family of operators generated by strongly continuous…
The use of operator-splitting methods to solve differential equations is widespread, but the methods are generally only defined for a given number of operators, most commonly two. Most operator-splitting methods are not generalizable to…
In this article we propose an optimal method referred to as SPlit for splitting a dataset into training and testing sets. SPlit is based on the method of Support Points (SP), which was initially developed for finding the optimal…
The likelihood functions for discretely observed nonlinear continuous-time models based on stochastic differential equations are not available except for a few cases. Various parameter estimation techniques have been proposed, each with…
The operator splitting method has been widely used to solve differential equations by splitting the equation into more manageable parts. In this work, we resolves a long-standing problem -- how to establish the stability of multi-product…
An initial-boundary value problem for the $n$-dimensional ($n\geq 2$) time-dependent Schr\"odinger equation in a semi-infinite (or infinite) parallelepiped is considered. Starting from the Numerov-Crank-Nicolson finite-difference scheme, we…