ISSN:
1572-9125
Keywords:
65 L 05
;
65 L 20
;
stability
;
contractivity
;
numerical solution of stiff initial value problems in ordinary differential equations
;
Runge-Kutta methods
;
Rosenbrock methods
;
rational Runge-Kutta methods
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract This paper concerns the stability analysis of numerical methods for approximating the solutions to (stiff) initial value problems. Our analysis includes the case of (nonlinear) systems of differential equations that are essentially more general than the classical test equationU′=λU, with λ a complex constant. We explore the relation between two stability concepts, viz. the concepts of contractivity and weak contractivity. General Runge-Kutta methods, one-stage Rosenbrock methods and a notable rational Runge-Kutta method are analysed in some detail.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01933735
