Related papers: Iterative operator-splitting methods for unbounded…
This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…
In this note unbounded hyperexpansive weighted composition operators are investigated. AS a consequence unbounded hyperexpansive multiplication and composition operators are characterized.
A dynamic iteration scheme for linear infinite-dimensional port-Hamiltonian systems is proposed. The dynamic iteration is monotone in the sense that the error is decreasing, it does not require any stability condition and is in particular…
We study an extension of the Distributive Full Non-associative Lambek Calculus with iterative division operators. The iterative operators can be seen as representing iterative composition of linguistic resources or of actions. A complete…
Variational regularization and the quasisolutions method are justified for unbounded closed, possibly nonlinear, operators. The argument is quite simple and yields general results.
In this paper we apply a scaling invariance analysis to reduce a class of parabolic moving boundary problems to free boundary problems governed by ordinary differential equations. As well known free boundary problems are always non-linear…
This paper describes an updated exponential Fourier based split-step method that can be applied to a greater class of partial differential equations than previous methods would allow. These equations arise in physics and engineering, a…
In this paper, we develop a class of samplers for the diffusion model using the operator-splitting technique. The linear drift term and the nonlinear score-driven drift of the probability flow ordinary differential equation are split and…
We investigate Lie-Trotter product formulae for abstract nonlinear evolution equations with delay. Using results from the theory of nonlinear contraction semigroups in Hilbert spaces, we explain the convergence of the splitting procedure.…
Splitting methods have emerged as powerful tools to address complex problems by decomposing them into smaller solvable components. In this work, we develop a general approach to forward-backward splitting methods for solving monotone…
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…
An equation containing a fractional power of an elliptic operator of second order is studied for Dirichlet boundary conditions. Finite difference approximations in space are employed. The proposed numerical algorithm is based on solving an…
We consider the numerical integration of non-autonomous separable parabolic equations using high order splitting methods with complex coefficients (methods with real coefficients of order greater than two necessarily have negative…
This contribution is dedicated to the exploration of exponential operator splitting methods for the time integration of evolution equations. It entails the review of previous achievements as well as the depiction of novel results. The…
Approximate solutions of the Fisher equation obtained by different splitting methods are investigated. The error of this nonlinear problem is analyzed. The order of different splitting methods coupled with numerical methods of different…
We analyze temporal approximation schemes based on overlapping domain decompositions. As such schemes enable computations on parallel and distributed hardware, they are commonly used when integrating large-scale parabolic systems. Our…
We prove a variant of the so-called bilinear embedding theorem for operators in divergence form with complex coefficients and with nonnegative locally integrable potentials, subject to mixed boundary conditions, and acting on arbitrary open…
We propose new local error estimators for splitting and composition methods. They are based on the construction of lower order schemes obtained at each step as a linear combination of the intermediate stages of the integrator, so that the…
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 general, high order splitting methods suffer from an order reduction phenomena when applied to the time integration of partial differential equations with non-periodic boundary conditions. In the last decade, there were introduced…