A step-size selection strategy for explicit Runge–Kutta methods based on Lyapunov exponent theory

Andrew J. Steyer ^[1] ; Erik S. Van Vleck ^[1]
1. [1] University of Kansas
  
  University of Kansas
  
  City of Lawrence, Estados Unidos
Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 292, Nº 1 (15 January 2016), 2016, págs. 703-719
Idioma: inglés
DOI: 10.1016/j.cam.2015.03.056
Enlaces
- Texto completo
Resumen
- Using a stability result for variable time-step Runge–Kutta methods applied to nonautonomous real linear scalar test problem that decays exponentially fast, a step-size selection algorithm is devised. The step-size selection algorithm is based partly on stability information obtained by estimating the discrete Lyapunov exponent of a Runge–Kutta method applied to a nonautonomous linear scalar problem. The utility of the approach is illustrated in numerical experiments that demonstrate how the new algorithm performs against a standard accuracy based step-size selection strategy.