Cheap error estimation for Runge-Kutta methods. (English) Zbl 0935.65074
This article investigates explicit Runge-Kutta pairs of orders \(p(q)\) with \(q<p-1\). This allows one to reduce the number of stages, while keeping the same order \(p\). The numerical experiments of the authors with pairs of orders between \(4\) and \(10\) demonstrate the efficiency of the new methods.
Reviewer: E.Hairer (Genève)
MSC:
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 65L50 | Mesh generation, refinement, and adaptive methods for ordinary differential equations |
| 65L70 | Error bounds for numerical methods for ordinary differential equations |
| 34A34 | Nonlinear ordinary differential equations and systems |
