### Abstract

We describe the construction of diagonally implicit multistage integration methods (DIMSIMs) of type 1 and 2 with the same stability properties as explicit Runge-Kutta methods or implicit SDIRK methods, respectively, of appropriate order. Such methods are intended for the numerical integration of nonstiff or stiff differential systems in a sequential computing environment. Examples of pqrst DIMSIMs are given with p, q, r,s ≤ 4 and t = 1 or 2, where p is the order, q is the stage order, r is the number of external stages, s is the number of internal stages, and t is the type of the method. Coefficients of the methods of order 4 were obtained numerically with the aid of continuation programs from PITCON, ALCON, and HOMPACK.

Original language | English (US) |
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Pages (from-to) | 385-415 |

Number of pages | 31 |

Journal | Applied Numerical Mathematics |

Volume | 21 |

Issue number | 4 |

DOIs | |

State | Published - Oct 1 1996 |

### Keywords

- A-stability
- General linear method
- Order conditions

### ASJC Scopus subject areas

- Numerical Analysis
- Computational Mathematics
- Applied Mathematics