### 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 1996 |

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### Keywords

- A-stability
- General linear method
- Order conditions

### ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics
- Modeling and Simulation

### Cite this

**Construction of diagonally implicit general linear methods of type 1 and 2 for ordinary differential equations.** / Butcher, J. C.; Jackiewicz, Zdzislaw.

Research output: Contribution to journal › Article

*Applied Numerical Mathematics*, vol. 21, no. 4, pp. 385-415. https://doi.org/10.1016/S0168-9274(96)00043-8

}

TY - JOUR

T1 - Construction of diagonally implicit general linear methods of type 1 and 2 for ordinary differential equations

AU - Butcher, J. C.

AU - Jackiewicz, Zdzislaw

PY - 1996/10

Y1 - 1996/10

N2 - 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.

AB - 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.

KW - A-stability

KW - General linear method

KW - Order conditions

UR - http://www.scopus.com/inward/record.url?scp=0030263281&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030263281&partnerID=8YFLogxK

U2 - 10.1016/S0168-9274(96)00043-8

DO - 10.1016/S0168-9274(96)00043-8

M3 - Article

AN - SCOPUS:0030263281

VL - 21

SP - 385

EP - 415

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

SN - 0168-9274

IS - 4

ER -