## Abstract

We consider the convergence and stability property of MUSCL relaxing schemes applied to conservation laws with stiff source terms. The maximum principle for the numerical schemes will be established. It will be also shown that the MUSCL relaxing schemes are uniformly l^{1}- and TV-stable in the sense that they are bounded by a constant independent of the relaxation parameter ε, the Lipschitz constant of the stiff source term and the time step Δt. The Lipschitz constant of the l^{1} continuity in time for the MUSCL relaxing schemes is shown to be independent of ε and Δt. The convergence of the relaxing schemes to the corresponding MUSCL relaxed schemes is then established.

Original language | English |
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Pages (from-to) | 173-195 |

Number of pages | 23 |

Journal | Journal of Scientific Computing |

Volume | 15 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jun 2000 |

## Scopus Subject Areas

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

## User-Defined Keywords

- Convergence
- Maximum principle
- Nonlinear conservation laws
- Relaxation scheme