## Abstract

The standard algebraic stability condition for general linear methods (GLMs) is considered in a modified form, and connected to a branch of Control Theory concerned with the discrete algebraic Riccati equation (DARE). The DARE theory shows that, for an algebraically stable method, there is a minimal G-matrix, G *, satisfying an equation, rather than an inequality. This result, and another alternative reformulation of algebraic stability, are applied to construct new GLMs with 2 steps and 2 stages, one of which has order p=4 and stage order q=3. The construction process is simplified by method-equivalence, and Butcher’s simplified order conditions for the case p≤q+1.

Original language | English |
---|---|

Pages (from-to) | 93-111 |

Number of pages | 19 |

Journal | BIT Numerical Mathematics |

Volume | 49 |

Issue number | 1 |

Early online date | 30 Jan 2009 |

DOIs | |

Publication status | Published - Mar 2009 |

## Keywords

- Discrete algebraic Riccati equation
- General linear methods
- Algebraic stability

## Fingerprint

Dive into the research topics of 'Algebraically stable general linear methods and the*G*-matrix'. Together they form a unique fingerprint.