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Parallel implicit-explicit general linear methods
High-order discretizations of partial differential equations (PDEs) nece...
02/03/2020 ∙ by Steven Roberts, et al. ∙
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On theoretical upper limits for valid timesteps of implicit ODE methods
Implicit methods for the numerical solution of initial-value problems ma...
12/18/2019 ∙ by K. R. Green, et al. ∙
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Continuous Galerkin Schemes for Semi-Explicit Differential-Algebraic Equations
This paper studies a new class of integration schemes for the numerical ...
11/18/2020 ∙ by Robert Altmann, et al. ∙
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Linearly implicit GARK schemes
Systems driven by multiple physical processes are central to many areas ...
08/04/2020 ∙ by Adrian Sandu, et al. ∙
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IMEX error inhibiting schemes with post-processing
High order implicit-explicit (IMEX) methods are often desired when evolv...
12/19/2019 ∙ by Adi Ditkowski, et al. ∙
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Implicit Gradient Neural Networks with a Positive-Definite Mass Matrix for Online Linear Equations Solving
Motivated by the advantages achieved by implicit analogue net for solvin...
03/17/2017 ∙ by Ke Chen, et al. ∙
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Staggered explicit-implicit time-discretization for elastodynamics with dissipative internal variables
An extension of the two-step staggered time discretization of linear ela...
06/09/2020 ∙ by Tomáš Roubíček, et al. ∙
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Convergence Results for Implicit–Explicit General Linear Methods
04/08/2020 ∙ by Adrian Sandu, et al. ∙
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This paper studies fixed-step convergence of implicit-explicit general linear methods. We focus on a subclass of schemes that is internally consistent, has high stage order, and favorable stability properties. Classical, index-1 differential algebraic equation, and singular perturbation convergence analyses results are given. For all these problems IMEX GLMs from the class of interest converge with the full theoretical orders under general assumptions. The convergence results require the time steps to be sufficiently small, with upper bounds that are independent on the stiffness of the problem.
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