Interpolants for Runge-Kutta formulas. (English) Zbl 0617.65068
To obtain a continuous approximate solution of an initial value problem of an ordinary differential equation, the authors give actual formulas by Hermite-Birkhoff interpolation (using derivatives as well as the functional values) for three typical Runge-Kutta (RK) formulas. All of the RK formulas are of embedded type formula-pairs, whose orders are (3,4), (4,5) and (5,6) respectively. Some of them need no extra functional evaluation, while the others need one or two extra evaluations. Several numerical examples are attached. They emphasize the importance to have continuous solution for practice.
Reviewer: S.Hitotumatu
MSC:
65L05 | Numerical methods for initial value problems involving ordinary differential equations |
65D05 | Numerical interpolation |
34A34 | Nonlinear ordinary differential equations and systems |