High-order convergence of spectral deferred correction methods on general quadrature nodes

Tao TANG*, Hehu Xie, Xiaobo Yin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)

Abstract

It has been demonstrated that spectral deferred correction (SDC) methods can achieve arbitrary high order accuracy and possess good stability properties. There have been some recent interests in using high-order Runge-Kutta methods in the prediction and correction steps in the SDC methods, and higher order rate of convergence is obtained provided that the quadrature nodes are uniform. The assumption of the use of uniform mesh has a serious practical drawback as the well-known Runge phenomenon may prevent the use of reasonably large number of quadrature nodes. In this work, we propose a modified SDC methods with high-order integrators which can yield higher convergence rates on both uniform and non-uniform quadrature nodes. The expected high-order of accuracy is theoretically verified and numerically demonstrated.

Original languageEnglish
Pages (from-to)1-13
Number of pages13
JournalJournal of Scientific Computing
Volume56
Issue number1
DOIs
Publication statusPublished - Jul 2013

Scopus Subject Areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • General quadrature nodes
  • High-order convergence
  • Modified SDC
  • Spectral deferred correction (SDC)

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