Free Access
Issue
ESAIM: M2AN
Volume 50, Number 4, July-August 2016
Page(s) 1137 - 1166
DOI https://doi.org/10.1051/m2an/2015072
Published online 07 July 2016
  1. W. Auzinger, H. Hofstätter, W. Kreuzer and E. Weinmüller, Modified defect correction algorithms for ODEs. Part I: General Theory. Numer. Algorithms 36 (2004) 135–156. [CrossRef] [MathSciNet] [Google Scholar]
  2. K. Böhmer and HJ Stetter, Defect correction methods. Theory and applications (1984). [Google Scholar]
  3. A. Christlieb, M. Morton, B. Ong and J.-M. Qiu, Semi-implicit integral deferred correction constructed with high order additive Runge–Kutta methods. Communications in Mathematical Sciences (2011). [Google Scholar]
  4. A. Christlieb, B. Ong and J.M. Qiu, Comments on high order integrators embedded within integral deferred correction methods. Commun. Appl. Math. Comput. Sci 4 (2009) 27–56. [CrossRef] [MathSciNet] [Google Scholar]
  5. A. Christlieb, B. Ong and J.M. Qiu, Integral deferred correction methods constructed with high order Runge–Kutta integrators. Math. Comput. 79 (2009) 761. [CrossRef] [Google Scholar]
  6. A. Dutt, L. Greengard and V. Rokhlin, Spectral deferred correction methods for ordinary differential equations. BIT Numer. Math. 40 (2000) 241–266. [CrossRef] [Google Scholar]
  7. C.W. Gear, Differential-algebraic equation index transformations. SIAM J. Sci. Stat. Comput. 9 (1988) 39–47. [CrossRef] [Google Scholar]
  8. E. Hairer and G. Wanner, Solving ordinary differential equations II: stiff and differential algebraic problems, vol. 2. Springer Verlag (1993). [Google Scholar]
  9. E. Hairer, C. Lubich and M. Roche, Error of Runge–Kutta methods for stiff problems studied via differential algebraic equations. BIT Numer. Math. 28 (1988) 678–700. [CrossRef] [Google Scholar]
  10. J. Huang, J. Jia and M. Minion, Arbitrary order Krylov deferred correction methods for differential algebraic equations. J. Comput. Phys. 221 (2007) 739–760. [CrossRef] [MathSciNet] [Google Scholar]
  11. A.T. Layton, On the choice of correctors for semi-implicit picard deferred correction methods. Appl. Numer. Math. 58 (2008) 845–858. [CrossRef] [MathSciNet] [Google Scholar]
  12. A.T. Layton and M.L. Minion, Implications of the choice of quadrature nodes for picard integral deferred corrections methods for ordinary differential equations. BIT Numer. Math. 45 (2005) 341–373. [CrossRef] [Google Scholar]
  13. A.T. Layton and M.L. Minion, Implications of the choice of predictors for semi-implicit picard integral deferred corrections methods. Commun. Appl. Math. Comput. Sci. 1 (2007) 1–34. [CrossRef] [Google Scholar]
  14. M.L. Minion, Semi-implicit spectral deferred correction methods for ordinary differential equations. Commun. Math. Sci. 1 (2003) 471–500. [CrossRef] [MathSciNet] [Google Scholar]
  15. R.E. O’Malley Jr, Introduction to singular perturbations, Vol. 14. Applied Mathematics and Mechanics. Technical report, DTIC Document (1974). [Google Scholar]
  16. R.D. Skeel, A theoretical framework for proving accuracy results for deferred corrections. SIAM J. Numer. Anal. 19 (1982) 171–196. [CrossRef] [MathSciNet] [Google Scholar]
  17. A. Tikhonov, B. Vasl’eva and A. Sveshnikov, Differential Equations. Springer Verlag (1985). [Google Scholar]

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