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

J. C. Butcher, Zdzislaw Jackiewicz

Research output: Contribution to journalArticle

49 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)385-415
Number of pages31
JournalApplied Numerical Mathematics
Volume21
Issue number4
DOIs
StatePublished - Oct 1996

Fingerprint

General Linear Methods
Implicit Method
Ordinary differential equations
Ordinary differential equation
Runge Kutta methods
Convergence of numerical methods
Stiff Systems
Explicit Methods
Runge-Kutta Methods
Differential System
Numerical integration
Continuation
Internal
Computing
Coefficient

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.

In: Applied Numerical Mathematics, Vol. 21, No. 4, 10.1996, p. 385-415.

Research output: Contribution to journalArticle

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