Journal of Scientific Computing

, Volume 25, Issue 1, pp 129–155 | Cite as

Implicit–Explicit Runge–Kutta Schemes and Applications to Hyperbolic Systems with Relaxation

  • Lorenzo Pareschi
  • Giovanni Russo


We consider new implicit–explicit (IMEX) Runge–Kutta methods for hyperbolic systems of conservation laws with stiff relaxation terms. The explicit part is treated by a strong-stability-preserving (SSP) scheme, and the implicit part is treated by an L-stable diagonally implicit Runge–Kutta method (DIRK). The schemes proposed are asymptotic preserving (AP) in the zero relaxation limit. High accuracy in space is obtained by Weighted Essentially Non Oscillatory (WENO) reconstruction. After a description of the mathematical properties of the schemes, several applications will be presented


Runge–Kutta methods hyperbolic systems with relaxation stiff systems high order shock capturing schemes 

AMS Subject Classification

65C20 82D25 


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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of FerraraFerraraItaly
  2. 2.Department of Mathematics and Computer ScienceUniversity of CataniaCataniaItaly

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