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Linear Multistep Methods for Impulsive Differential Equations [PDF]
Discrete Dynamics in Nature and Society, 2012 This paper deals with the convergence and stability of linear multistep methods for impulsive differential equations. Numerical experiments demonstrate that both the mid-point rule and two-step BDF method are of order p=0 when applied to impulsive ...
X. Liu, M. H. Song, M. Z. Liu
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On the contractivity of implicit–explicit linear multistep methods [PDF]
Applied Numerical Mathematics, 2002 Stability properties of implicit-explicit linear multistep methods (IMEX) are analyzed for the case of initial value problems for ordinary differential equations composed of stiff and nonstiff parts. In particular, the paper deals with contractivity and strong stability of the iterative process in the case of the linear autonomous test problem and an ...
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Journal of Algorithms & Computational Technology, 2012 This paper considers family of A(α)-stable second derivative linear multistep methods of order p = k + 3 for step number k ≥ 15 for the solution of stiff IVPs in ODEs. The methods are demonstrated to be A(α)-stable for k ≥ 13.
R. I. Okuonghae, M. N. O. Ikhile
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Discovery of Dynamics Using Linear Multistep Methods [PDF]
SIAM Journal on Numerical Analysis, 2021 Linear multistep methods (LMMs) are popular time discretization techniques for the numerical solution of differential equations. Traditionally they are applied to solve for the state given the dynamics (the forward problem), but here we consider their application for learning the dynamics given the state (the inverse problem).
Rachael T. Keller, Qiang Du 0001
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Mathematics, 2021 In this paper, a symmetric eight-step predictor method (explicit) of 10th order is presented for the numerical integration of IVPs of second-order ordinary differential equations. This scheme has variable coefficients and can be used as a predictor stage
Ali Shokri +4 more
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Global error estimation of linear multistep methods through the Runge-Kutta methods [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2016 In this paper, we study the global truncation error of the linear multistep methods (LMM) in terms of local truncation error of the corresponding Runge-Kutta schemes. The key idea is the representation of LMM with a corresponding Runge-Kutta method.
Javad Farzi
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Probabilistic Linear Multistep Methods [PDF]
CoRR, 2016 We present a derivation and theoretical investigation of the Adams-Bashforth and Adams-Moulton family of linear multistep methods for solving ordinary differential equations, starting from a Gaussian process (GP) framework. In the limit, this formulation coincides with the classical deterministic methods, which have been used as higher-order initial ...
Onur Teymur +2 more
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Monotonicity-Preserving Linear Multistep Methods [PDF]
SIAM Journal on Numerical Analysis, 2003 The authors consider several linear multistep methods for ordinary differential equations and provide an analysis of their monotonicity properties, which mainly include positivity and the diminishing of total variation. It is shown that suitable starting procedures allow for statements on monotonicity for important classes of methods not covered by ...
Willem Hundsdorfer +2 more
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Semi-Implicit Multistep Extrapolation ODE Solvers
Mathematics, 2020 Multistep methods for the numerical solution of ordinary differential equations are an important class of applied mathematical techniques. This paper is motivated by recently reported advances in semi-implicit numerical integration methods, multistep and
Denis Butusov +4 more
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Numerical Stability and Performance of Semi-Explicit and Semi-Implicit Predictor–Corrector Methods
Mathematics, 2022 Semi-implicit multistep methods are an efficient tool for solving large-scale ODE systems. This recently emerged technique is based on modified Adams–Bashforth–Moulton (ABM) methods.
Loïc Beuken +4 more
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