Journal of Scientific Computing

, Volume 63, Issue 3, pp 633–653 | Cite as

Error Analysis of Explicit Partitioned Runge–Kutta Schemes for Conservation Laws

  • Willem HundsdorferEmail author
  • David I. Ketcheson
  • Igor Savostianov


An error analysis is presented for explicit partitioned Runge–Kutta methods and multirate methods applied to conservation laws. The interfaces, across which different methods or time steps are used, lead to order reduction of the schemes. Along with cell-based decompositions, also flux-based decompositions are studied. In the latter case mass conservation is guaranteed, but it will be seen that the accuracy may deteriorate.


Multirate methods Partitioned Runge–Kutta methods  Conservation Stability Convergence 

Mathematics Subject Classification

65L06 65M06 65M20 



This paper originated from work of W. H. with Anna Mozartova and Valeriu Savcenco. The contributions of Mozartova and Savcenco, on the design of multirate methods and monotonicity properties of these methods, are contained in [6]. They are thanked for helpful comments on preliminary convergence results for first-order methods.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Willem Hundsdorfer
    • 1
    Email author
  • David I. Ketcheson
    • 2
  • Igor Savostianov
    • 1
  1. 1.CWIAmsterdamThe Netherlands
  2. 2.Division Mathematical and Computer Sciences and EngineeringKing Abdullah University of Science and Technology (KAUST)ThuwalSaudi Arabia

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