Order Results for Mono-Implicit Runge-Kutta Methods

The mono-implicit Runge-Kutta methods are a subclass of the well-known implicit Runge-Kutta methods and have application in the efficient numerical solution of systems of initial and boundary value ordinary differential equations. Although the efficiency and stability properties of this class of met...

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Bibliographic Details
Published in:SIAM journal on numerical analysis 1994-06, Vol.31 (3), p.876-891
Main Authors: Burrage, K., Chipman, F. H., Muir, P. H.
Format: Article
Language:English
Subjects:
Applied mathematics
Approximation
Boundary value problems
Butchering
Cash
Coefficients
Exact sciences and technology
Mathematics
Matrices
Methods
Numerical analysis
Numerical analysis. Scientific computation
Odes
Ordinary differential equations
Runge Kutta method
Sciences and techniques of general use
Tableaux
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Summary:The mono-implicit Runge-Kutta methods are a subclass of the well-known implicit Runge-Kutta methods and have application in the efficient numerical solution of systems of initial and boundary value ordinary differential equations. Although the efficiency and stability properties of this class of methods have been studied in a number of papers, the specific question of determining the maximum order of an s-stage mono-implicit Runge-Kutta method has not been dealt with. In addition to the complete characterization of some subclasses of these methods having a number of stages s ≤ 5, a main result of this paper is a proof that the order of an s-stage mono-implicit Runge-Kutta method is at most s + 1.
ISSN:0036-1429
1095-7170
DOI:10.1137/0731047