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

作者：Steyer Andrew J; Van Vleck Erik S^*

来源：Journal of Computational and Applied Mathematics, 2016, 292: 703-719.

DOI：10.1016/j.cam.2015.03.056

• Numerical stability analysis
• Lyapunov exponents
• Runge-Kutta methods
• Step-size selection

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.

• 出版日期2016-1-15