论文信息 - Relationships among some classes of implicit Runge-Kutta methods and their stability functions

Relationships among some classes of implicit Runge-Kutta methods and their stability functions

In this paper we apply the theory for implicit Runge-Kutta methods presented by Stetter to a number of subclasses of methods that have recently been discussed in the literature. We first show how each of these classes can be expressed within this theoretical framework and from this we are able to establish a number of relationships among these classes. In addition to improving the current state of understanding of these methods, their expression within this theoretical framework makes it possible for us to obtain results giving general forms for their stability functions.

W. H. Enright | P. H. Muir

[1] H. Stetter. Analysis of Discretization Methods for Ordinary Differential Equations , 1973 .

[2] M. N. Spijker,et al. A note onB-stability of Runge-Kutta methods , 1980 .

[3] Rudolf Scherer,et al. Reflected and transposed Runge-Kutta methods , 1983 .

[4] David J. Moore,et al. A high order method for the numerical solution of two-point boundary value problems , 1980 .

[5] John C. Butcher,et al. An algebraic theory of integration methods , 1972 .

[6] J. Cash,et al. Mono-implicit Runge—Kutta Formulae for the Numerical Integration of Stiff Differential Systems , 1982 .

[7] Jeff R. Cash,et al. A Class of Implicit Runge-Kutta Methods for the Numerical Integration of Stiff Ordinary Differential Equations , 1975, JACM.

[8] W.M.G. van Bokhoven,et al. Efficient higher order implicit one-step methods for integration of stiff differential equations , 1980 .

[9] J. Butcher. Implicit Runge-Kutta processes , 1964 .

[10] J. Cash,et al. High order methods for the numerical solution of two-point boundary value problems , 1982 .

[11] Suchitra Gupta,et al. An Adaptive Boundary Value Runge–Kutta Solver for First Order Boundary Value Problems , 1985 .

[12] John C. Butcher,et al. An application of the runge-kutta space , 1984 .