Related papers: Estimating Global Errors in Time Stepping

Semi-Lagrangian methods are numerical methods designed to find approximate solutions to particular time-dependent partial differential equations (PDEs) that describe the advection process. We propose semi-Lagrangian one-step methods for…

We investigate model assessment and selection in a changing environment, by synthesizing datasets from both the current time period and historical epochs. To tackle unknown and potentially arbitrary temporal distribution shift, we develop…

Model reduction is a powerful tool in dealing with numerical simulation of large scale dynamic systems for studying complex physical systems. Two major types of model reduction methods for linear time-invariant dynamic systems are Krylov…

In 1986, Dixon and McKee developed a discrete fractional Gr\"{o}nwall inequality [Z. Angew. Math. Mech., 66 (1986), pp. 535--544], which can be seen as a generalization of the classical discrete Gr\"{o}nwall inequality. However, this…

This work presents algorithms for the efficient implementation of discontinuous Galerkin methods with explicit time stepping for acoustic wave propagation on unstructured meshes of quadrilaterals or hexahedra. A crucial step towards…

A complete error analysis of variational integrators is obtained, by blowing up the discrete variational principles, all of which have a singularity at zero time-step. Divisions by the time step lead to an order that is one less than…

When one wishes to numerically solve an initial value problem, it is customary to rewrite it as an equivalent first-order system to which a method, usually from the class of Runge-Kutta methods, is applied. Directly treating higher-order…

We describe a method to execute globally controlled quantum information processing which admits a fault tolerant quantum error correction scheme. Our scheme nominally uses three species of addressable two-level systems which are arranged in…

Data-driven methods that detect anomalies in times series data are ubiquitous in practice, but they are in general unable to provide helpful explanations for the predictions they make. In this work we propose a model-agnostic algorithm that…

Inverse problems use physical measurements along with a computational model to estimate the parameters or state of a system of interest. Errors in measurements and uncertainties in the computational model lead to inaccurate estimates. This…

This paper continues to study the explicit two-stage fourth-order accurate time discretiza- tions [5, 7]. By introducing variable weights, we propose a class of more general explicit one-step two-stage time discretizations, which are…

The present work provides a comprehensive study of symmetric-conjugate operator splitting methods in the context of linear parabolic problems and demonstrates their additional benefits compared to symmetric splitting methods. Relevant…

Spectral Deferred Correction (SDC) is an iterative method for the numerical solution of ordinary differential equations. It works by refining the numerical solution for an initial value problem by approximately solving differential…

We describe new implementations of quantum error correction that are continuous in time, and thus described by continuous dynamical maps. We evaluate the performance of such schemes using numerical simulations, and comment on the…

This work proposes a discretization of the acoustic wave equation with possibly oscillatory coefficients based on a superposition of discrete solutions to spatially localized subproblems computed with an implicit time discretization. Based…

The problem of change-point estimation is considered under a general framework where the data are generated by unknown stationary ergodic process distributions. In this context, the consistent estimation of the number of change-points is…

We consider continuous and discontinuous Galerkin time stepping methods of arbitrary order as applied to nonlinear initial value problems in real Hilbert spaces. Our only assumption is that the nonlinearities are continuous; in particular,…

Solving Linear Ordinary Differential Equations (ODEs) plays an important role in many applications. There are various numerical methods and solvers to obtain approximate solutions. However, few work about global error estimation can be…

We present an approach for the efficient implementation of self-adjusting multi-rate Runge-Kutta methods and we introduce a novel stability analysis, that covers the multi-rate extensions of all standard Runge-Kutta methods and allows to…

Classical and new numerical schemes are generated using evolutionary computing. Differential Evolution is used to find the coefficients of finite difference approximations of function derivatives, and of single and multi-step integration…