Spectral Deferred Correction Methods for Ordinary Differential Equations

By A. Dutt, Leslie Greengard, Vladimir Rokhlin. 2000

483 citations recorded by the source corpus.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/2890a4022320da137611870ae6ba94c3b9816f9c

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In Computational Mechanics

1. Chi-Wang Shu
2. Randall J. LeVeque
3. Yan Xu
4. Jie Shen
5. Jie Xu
6. Jiang Yang
7. Michael L. Minion
8. Benjamin W. Ong

In Electrical and Electronic Engineering

1. Chi-Wang Shu
2. Yan Xu
3. Anita T. Layton
4. Benjamin W. Ong
5. Andrew J. Christlieb
6. David I. Ketcheson
7. Sigal Gottlieb
8. Anne Bourlioux

In Numerical Analysis

1. Chi-Wang Shu
2. Yan Xu
3. Benjamin W. Ong
4. Randall J. LeVeque
5. Andrew J. Christlieb
6. Anita T. Layton
7. Jie Shen
8. Michael L. Minion

Citations in the corpus

• Implications of the Choice of Quadrature Nodes for Picard Integral Deferred Corrections Methods for Ordinary Differential Equations (2005, methodology): “As mentioned before, the points tm are chosen in [10] to be the standard Gaussian quadrature nodes, and the solution is only computed at these nodes on the interior of the interval.”
• A Parallel Space-Time Algorithm (2012, methodology): “It was shown previously in [10] that successive application of the correction procedure not only increases the accuracy of the solution, but also increases the formal order of accuracy of the scheme.”
• High-order multi-implicit spectral deferred correction methods for problems of reactive flow (2003, methodology): “MISDC methods, which are a generalization of SI spectral deferred correction (SDC) methods introduced in [19] (which are in turn modifications of the explicit and implicit SDC methods appearing in [11]), use a low-order numerical method to compute a highorder approximation.”
• The scalar auxiliary variable (SAV) approach for gradient flows (2018, background): “One can also use the spectral deferred correction (SDC) [7] to takes a correction technique to enhance the accuracy of the stabilized scheme, but it still fails to preserve the nonlinear energy stability [11].”
• Local Discontinuous Galerkin Methods for High-Order Time-Dependent Partial Differential Equations (2009, methodology): “1 The spectral deferred correction method Dutt, Greengard and Rokhlin presented a new variation of the classical method of deferred correction, called the spectral deferred correction (SDC) method, in [49].”
• Semi-implicit spectral deferred correction methods for ordinary differential equations (2003, methodology): “This is slightly different than the notation in [13], but has the benefit that an SISDC P method has global order of accuracy min(K, P ).”
• Finite difference methods for ordinary and partial differential equations - steady-state and time-dependent problems (2007, methodology): “One time-stepping procedure that has the flavor of a spectral procedure in time is the recent spectral deferred correction method presented in [28].”
• High Order Strong Stability Preserving Time Discretizations (2009, methodology): “In this section we survey the recent work [60] on the study of the SSP property of a newly developed time discretization technique, namely the (spectral) deferred correction (DC) method constructed in [17].”