On Spurious Fixed Points of Runge–Kutta Methods

✍ Scribed by F. Vadillo

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 474 KB
• Volume: 132
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1996.5615

✦ Synopsis

In this paper we investigate the onset of spurious fixed points when Runge-Kutta methods are applied to study the dynamics of equation. Iserles [20] showed the existence of spurious differential equations. It is shown computationally that the spurious fixed points in Runge-Kutta methods and predictorequilibria of Griffiths et al. [14] are connected at infinity with fixed corrector methods. points inherited from the differential equation. We introduce and In this paper we shall consider Runge-Kutta methods study the concept of B-regularity which is in connection to the applied to the autonomous scalar initial-value problem concept of regularity introduced by Iserles. ᮊ 1997 Academic Press Principium cuius hinc nobis exordia sumet, uЈ ϭ f(u), t Ն t 0 , (1.1) nullam rem e nilo gigni diuinitus umquam. Nam si de nilo fierent, ex omnibus' rebus u(t 0 ) ϭ u 0 . omne genus nasci posset, nil semine egeret. De rerum natura, Liber Primus, 149. Lucrecio This problem has a fixed point u*, also known as equilibrium point, critical point, or steady-state solution, when 78