Implicit-Explicit Methods for Time-Dependent PDE''s
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TL;DR: Numerical experiments demonstrate that weak decay of high frequency modes can lead to extra iterations on the finest grid when using multigrid computations with finite difference spatial discretization, and to aliasing when using spectral collocation for spatialDiscretization.
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About: This article is published in Journal of Applied Mathematics and Mechanics. The article was published on 01 May 1993. and is currently open access. The article focuses on the topics: Flux limiter & Multigrid method.
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Citations
Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
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Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation
Lorenzo Pareschi,Giovanni Russo +1 more
TL;DR: In this article, new implicit-explicit (IMEX) Runge-Kutta methods were proposed for hyperbolic systems of conservation laws with stiff relaxation terms. But the implicit part is treated by a strong-stability-preserving (SSP) scheme, and the explicit part is represented by an L-stable diagonally implicit Runge Kutta method (DIRK).
363
Semi-implicit spectral deferred correction methods for ordinary differential equations
TL;DR: The results suggest that higher-order SISDC methods are more efficient than semi-implicit Runge-Kutta methods for moderately stiff problems in terms of accuracy per function evaluation.
Implicit-explicit methods for reaction-diffusion problems in pattern formation
TL;DR: This work analyzes the performance of several of the best known linear multistep IMEX schemes for reaction-diffusion problems in pattern formation and finds that first order accurate schemes, as well as schemes which produce only a weak decay of high frequency spatial error may yield plausible results which are nonetheless qualitatively incorrect.
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