Related papers: Symmetric general linear methods
Although convergence of the Parareal and multigrid-reduction-in-time (MGRIT) parallel-in-time algorithms is well studied, results on their optimality is limited. Appealling to recently derived tight bounds of two-level Parareal and MGRIT…
Dedicated treatment of symmetries in satisfiability problems (SAT) is indispensable for solving various classes of instances arising in practice. However, the exploitation of symmetries usually takes a black box approach. Typically,…
In this paper we construct higher-order variational integrators for a class of degenerate systems described by Lagrangians that are linear in velocities. We analyze the geometry underlying such systems and develop the appropriate theory for…
In this paper, exponential Runge-Kutta methods of collocation type (ERKC) which were originally proposed in (Appl Numer Math 53:323-339, 2005) are extended to semilinear parabolic problems with time-dependent delay. Two classes of the ERKC…
We prove generalizations of the first and second Ray-Knight theorems, for a large class of non-symmetric strong Markov processes. These results link the local times of the Markov process with the squares of associated Gaussian processes.…
Time-reversal symmetry is a prevalent feature of microscopic physics, including operational quantum theory and classical general relativity. Previous works have studied indefinite causal structure using the language of operational quantum…
Symmetry is a key property of numerical methods. The geometric properties of symmetric schemes make them an attractive option for integrating Hamiltonian systems, whilst their ability to exactly recover the initial condition without the…
This article proposes a new class of general linear method with $p=q$ and $r=s=p+1$. The construction of the present method is carried out using order conditions and error minimization subject to $A$- stability constraints. The proposed…
For interacting classical field theories such as general relativity exact solutions typically can only be found by imposing physically motivated (Killing) {\it symmetry} assumptions. Such highly symmetric solutions are then often used as…
When applied to stiff, linear differential equations with time-dependent forcing, Runge-Kutta methods can exhibit convergence rates lower than predicted by the classical order condition theory. Commonly, this order reduction phenomenon is…
Time-parallel algorithms, such as Parareal, are well-understood for linear problems, but their convergence analysis for nonlinear, chaotic systems remains limited. This paper introduces a new theoretical framework for analysing…
This work focuses on the development of a new class of high-order accurate methods for multirate time integration of systems of ordinary differential equations. The proposed methods are based on a specific subset of explicit one-step…
In this article, we analyze three classes of time-reversal of a Markov process with Gaussian noise on a manifold. We first unveil a commutativity constraint for the most general of these time-reversals to be well defined. Then we give a…
Splitting-based time integration approaches such as fractional steps, alternating direction implicit, operator splitting, and locally one-dimensional methods partition the system of interest into components and solve individual components…
Implicit Runge--Kutta (IRK) methods are highly effective for solving stiff ordinary differential equations (ODEs) but can be computationally expensive for large-scale problems due to the need of solving coupled algebraic equations at each…
The generalized additive Runge-Kutta (GARK) framework provides a powerful approach for solving additively partitioned ordinary differential equations. This work combines the ideas of symplectic GARK schemes and multirate GARK schemes to…
This work generalizes the additively partitioned Runge-Kutta methods by allowing for different stage values as arguments of different components of the right hand side. An order conditions theory is developed for the new family of…
For a large class of fully nonlinear parabolic equations, which include gradient flows for energy functionals that depend on the solution gradient, the semidiscretization in time by implicit Runge-Kutta methods such as the Radau IIA methods…
We study the problem of determining whether a given temporal specification can be implemented by a symmetric system, i.e., a system composed from identical components. Symmetry is an important goal in the design of distributed systems,…
We propose an experimental study of adaptive time-stepping methods for efficient modeling of the aggregation-fragmentation kinetics. Precise modeling of this phenomena usually requires utilization of the large systems of nonlinear ordinary…