### Abstract

We investigate some classes of general linear methods with s internal and r external approximations, with stage order q and order p, adjacent to the class with s=r=q=p considered by Butcher. We demonstrate that interesting methods exist also if s+1=r=q, p=q or q+1, s=r+1=q, p=q or q+1, and s=r=q, p=q+1. Examples of such methods are constructed with stability function matching the A-acceptable generalized Padé approximations to the exponential function.

Original language | English (US) |
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Pages (from-to) | 452-472 |

Number of pages | 21 |

Journal | BIT |

Volume | 33 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1 1993 |

### Keywords

- General linear method
- Subject classifications: AMS(MOS), 65L05, 65L07
- order conditions
- stability analysis

### ASJC Scopus subject areas

- Software
- Computer Graphics and Computer-Aided Design
- Computational Mathematics
- Applied Mathematics

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## Cite this

Butcher, J. C., & Jackiewicz, Z. (1993). Diagonally implicit general linear methods for ordinary differential equations.

*BIT*,*33*(3), 452-472. https://doi.org/10.1007/BF01990528