Linear multistep methods for optimal control problems and applications to hyperbolic relaxation systems [PDF]
, 2018 We are interested in high-order linear multistep schemes for time discretization of adjoint equations arising within optimal control problems. First we consider optimal control problems for ordinary differential equations and show loss of accuracy for ...
Albi, Giacomo +2 more
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Direct and Indirect Couplings in Coherent Feedback Control of Linear Quantum Systems [PDF]
, 2011 The purpose of this paper is to study and design direct and indirect couplings for use in coherent feedback control of a class of linear quantum stochastic systems.
James, Matthew R., Zhang, Guofeng
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Stability of one-step and linear multistep methods - a matrix technique approach
Electronic Journal of Qualitative Theory of Differential Equations, 2016 We investigate the stability of one-step and linear multistep methods from a new direction. Our aim is to modify the long and technical proof which is consequently omitted in almost every textbook and make it user-friendly.
Miklós Emil Mincsovics
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Exponential Multistep Methods for Stiff Delay Differential Equations
Axioms, 2022 Stiff delay differential equations are frequently utilized in practice, but their numerical simulations are difficult due to the complicated interaction between the stiff and delay terms.
Rui Zhan +3 more
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Linear multistep methods and global Richardson extrapolation
Applied Mathematics Letters, 2022 In this work, we study the application the classical Richardson extrapolation (RE) technique to accelerate the convergence of sequences resulting from linear multistep methods (LMMs) for solving initial-value problems of systems of ordinary differential equations numerically.
Imre Fekete, Lajos Lóczi
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On overcoming Dahlquist’s second barrier for$A$-stable linear multistep methods [PDF]
Iranian Journal of Numerical Analysis and OptimizationDahlquist’s second barrier limits the order of $A$-stable linear multistep methods to at most two, posing significant challenges for achieving higher accuracy in the numerical solution of stiff ordinary differential equations.
G. Hojjati, S. Fazeli, A. Moradi
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Estimation of Longest Stability Interval for a Kind of Explicit Linear Multistep Methods
Discrete Dynamics in Nature and Society, 2010 The new explicit linear three-order four-step methods with longest interval of absolute stability are proposed. Some numerical experiments are made for comparing different kinds of linear multistep methods.
Y. Xu, J. J. Zhao
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Multigrid Waveform Relaxation on Spatial Finite Element Meshes: The Discrete-Time Case [PDF]
, 1996 The efficiency of numerically solving time-dependent partial differential equations on parallel computers can be greatly improved by computing the solution on many time levels simultaneously.
Janssen, Jan, Vandewalle, Stefan
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Full linear multistep methods as root-finders [PDF]
Applied Mathematics and Computation, 2018 Root-finders based on full linear multistep methods (LMMs) use previous function values, derivatives and root estimates to iteratively find a root of a nonlinear function. As ODE solvers, full LMMs are typically not zero-stable. However, used as root-finders, the interpolation points are convergent so that such stability issues are circumvented.
Bart S. van Lith +2 more
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On monotonicity and boundedness properties of linear multistep methods [PDF]
Mathematics of Computation, 2005 In this paper an analysis is provided of nonlinear monotonicity and boundedness properties for linear multistep methods. Instead of strict monotonicity for arbitrary starting values we shall focus on generalized monotonicity or boundedness with Runge-Kutta starting procedures.
Willem Hundsdorfer, Steven J. Ruuth
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