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Time integration methods for solving initial value problems are an important component of many scientific and engineering simulations. Implicit time integrators are desirable for their stability properties, significantly relaxing…

Numerical Analysis · Mathematics 2020-11-24 Ross Glandon , Mahesh Narayanamurthi , Adrian Sandu

We use backward error analysis for differential equations to obtain modified or distorted equations describing the behaviour of the Newmark scheme applied to the transient structural dynamics equation. Based on the newly derived distorted…

Numerical Analysis · Mathematics 2024-11-12 Donát M. Takács , Tamás Fülöp

We prove sharp, computable error estimates for the propagation of errors in the numerical solution of ordinary differential equations. The new estimates extend previous estimates of the influence of data errors and discretisation errors…

Numerical Analysis · Mathematics 2015-04-28 Benjamin Kehlet , Anders Logg

In engineering, accurately modeling nonlinear dynamic systems from data contaminated by noise is both essential and complex. Established Sequential Monte Carlo (SMC) methods, used for the Bayesian identification of these systems, facilitate…

Machine Learning · Statistics 2024-04-25 Joe D. Longbottom , Max D. Champneys , Timothy J. Rogers

Several construction methods for rational approximations to functions of one real variable are described in the present paper; the computational results that characterize the comparative accuracy of these methods are presented; an effect of…

Numerical Analysis · Mathematics 2025-10-20 Grigori Litvinov

To obtain strong convergence rates of numerical schemes, an overwhelming majority of existing works impose a global monotonicity condition on coefficients of SDEs. Nevertheless, there are still many SDEs from applications that do not have…

Numerical Analysis · Mathematics 2025-04-03 Lei Dai , Xiaojie Wang

In this contribution we develop an efficient reduced order model for solving parametrized linear-quadratic optimal control problems with linear time-varying state system. The fully reduced model combines reduced basis approximations of the…

Numerical Analysis · Mathematics 2024-08-29 Hendrik Kleikamp , Lukas Renelt

Stochastic differential equations (sdes) play an important role in physics but existing numerical methods for solving such equations are of low accuracy and poor stability. A general strategy for developing accurate and efficient schemes…

Quantum Physics · Physics 2009-11-10 Joshua Wilkie

Under suitable conditions, one-step generalized method of moments (GMM) based on the first-difference (FD) transformation is numerically equal to one-step GMM based on the forward orthogonal deviations (FOD) transformation. However, when…

Econometrics · Economics 2018-08-21 Robert F. Phillips

A method for adaptive model order reduction for nonsmooth discrete element simulation is developed and analysed in numerical experiments. Regions of the granular media that collectively move as rigid bodies are substituted with rigid bodies…

Computational Physics · Physics 2015-12-02 Martin Servin , Da Wang

Building on the successes of local kernel methods for approximating the solutions to partial differential equations (PDE) and the evaluation of definite integrals (quadrature/cubature), a local estimate of the error in such approximations…

Numerical Analysis · Mathematics 2023-08-30 Jonah A. Reeger

This paper develops a probabilistic numerical method for solution of partial differential equations (PDEs) and studies application of that method to PDE-constrained inverse problems. This approach enables the solution of challenging inverse…

Methodology · Statistics 2017-07-12 Jon Cockayne , Chris Oates , Tim Sullivan , Mark Girolami

We present here a general method based on the investigation of the relative energy of the system, that provides an unconditional error estimate for the approximate solution of the barotropic Navier Stokes equations obtained by time and…

Numerical Analysis · Mathematics 2015-04-14 Thierry Gallouet , Raphaele Herbin , David Maltese , Antonin Novotny

This paper proposes several explicit and implicit multistep frequency response optimized integrators considering first or second order derivative. A prediction-based method aiming at accelerating a novel power system transient simulation…

Systems and Control · Electrical Eng. & Systems 2021-02-16 Sheng Lei , Alexander Flueck

This study focuses on the numerical discretization methods for the continuous-time discounted linear-quadratic optimal control problem (LQ-OCP) with time delays. By assuming piecewise constant inputs, we formulate the discrete system…

Optimization and Control · Mathematics 2024-07-29 Zhanhao Zhang , Steen Hørsholt , John Bagterp Jørgensen

We present an error analysis of weak convergence of one-step numerical schemes for stochastic differential equations (SDEs) with super-linearly growing coefficients. Following Milstein's weak error analysis on the one-step approximation of…

Numerical Analysis · Mathematics 2023-03-29 Xiaojie Wang , Yuying Zhao , Zhongqiang Zhang

We present an error analysis of weak convergence of one-step numerical schemes for stochastic differential equations (SDEs) with super-linearly growing coefficients. Following Milstein's weak error analysis on the one-step approximation of…

Numerical Analysis · Mathematics 2023-03-29 Xiaojie Wang , Yuying Zhao , Zhongqiang Zhang

Motivated by the idea of imposing paralleling computing on solving stochastic differential equations (SDEs), we introduce a new Domain Decomposition Scheme to solve forward-backward stochastic differential equations (FBSDEs) parallely. We…

Numerical Analysis · Mathematics 2010-08-03 Minh-Binh Tran

In the domain of physics experiments, data fitting is a pivotal technique for extracting insights from both experimental and simulated datasets. This article presents an approximation method designed to estimate the systematic errors…

Data Analysis, Statistics and Probability · Physics 2024-02-29 Lu Li

In the paper an efficient semi-analytical approach based on the method of steps and differential transformation is proposed for numerical approximation of solutions of retarded logistic models of delayed and neutral type, including models…

Numerical Analysis · Mathematics 2019-01-14 Josef Rebenda , Zdeněk Šmarda