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ADER–Runge–Kutta Schemes for Conservation Laws in One Space Dimension

In: Hyperbolic Problems: Theory, Numerics, Applications

Author

Listed:
  • G. Russo

    (Università di Catania, Department of Mathematics and Computer Science)

  • E. F. Toro

    (University of Trento, Laboratory of Applied Mathematics)

  • V. A. Titarev

    (University of Trento)

Abstract

ADER is a recent Godunov-type approach for constructing arbitrarily highorder finite-volume schemes for hyperbolic conservation laws. The idea was first proposed for the constant coefficient linear advection equation in multiple space dimensions [12]. The extension to nonlinear systems is based on the approximate solution procedure for the so-called derivative Riemann problem [13, 14] for nonlinear hyperbolic systems with reactive source terms. For the resulting schemes see [11, 9, 2] and references therein.

Suggested Citation

  • G. Russo & E. F. Toro & V. A. Titarev, 2008. "ADER–Runge–Kutta Schemes for Conservation Laws in One Space Dimension," Springer Books, in: Sylvie Benzoni-Gavage & Denis Serre (ed.), Hyperbolic Problems: Theory, Numerics, Applications, pages 929-936, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-75712-2_97
    DOI: 10.1007/978-3-540-75712-2_97
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