Error Inhibiting Block One-step Schemes for Ordinary Differential Equations

作者： | A. Ditkowski, S. Gottlieb |

作者单位： |
^{1}Tel Aviv University^{2}University of Massachusetts, Dartmouth |

刊名： | Journal of Scientific Computing, 2017, Vol.73 (2-3), pp.691-711 |

来源数据库： | Springer Journal |

DOI： | 10.1007/s10915-017-0441-8 |

关键词： | ODE solvers; General linear methods; One-step methods; Global error; Local truncation error; Error inhibiting schemes; |

英文摘要： | The commonly used one step methods and linear multi-step methods all have a global error that is of the same order as the local truncation error (as defined in [ 1 , 6 , 8 , 13 , 15 ]). In fact, this is true of the entire class of general linear methods. In practice, this means that the order of the method is typically defined solely by order conditions which are derived by studying the local truncation error. In this work we investigate the interplay between the local truncation error and the global error, and develop a methodology which defines the construction of explicit error inhibiting block one-step methods (alternatively written as explicit general linear methods [ 2 ]). These error inhibiting schemes are constructed so that the accumulation of the local truncation error over time... |

原始语种摘要： | The commonly used one step methods and linear multi-step methods all have a global error that is of the same order as the local truncation error (as defined in [ 1 , 6 , 8 , 13 , 15 ]). In fact, this is true of the entire class of general linear methods. In practice, this means that the order of the method is typically defined solely by order conditions which are derived by studying the local truncation error. In this work we investigate the interplay between the local truncation error and the global error, and develop a methodology which defines the construction of explicit error inhibiting block one-step methods (alternatively written as explicit general linear methods [ 2 ]). These error inhibiting schemes are constructed so that the accumulation of the local truncation error over time... |