Practical aspects of interpolation in Runge-Kutta codes. (English) Zbl 0621.65067
The behaviour of interpolants within the step in applying Runge-Kutta codes is studied. An emphasis is put to the preservation of properties inherent in the computed solution. It is shown e.g. how to preserve the local monotonicity. The results discussed in this paper seem to be of considerable practical interest, especially to those implementing and developing ODE solvers.
Reviewer: V.A.Velev
MSC:
65L05 | Numerical methods for initial value problems involving ordinary differential equations |
34A34 | Nonlinear ordinary differential equations and systems |