Numerical methods for \(y''=f(x,y)\). (English) Zbl 0847.65051
Bainov, D. (ed.) et al., Proceedings of the first international colloquium on numerical analysis, Plovdiv, Bulgaria, August 13-17, 1992. Utrecht: VSP. 27-38 (1993).
Summary: This is a survey of direct methods for initial value problems involving ordinary differential equations of second order in which the first derivative does not appear explicitly. The emphasis is on problems having oscillatory solutions. The main classes of numerical methods for such problems are described and then consideration is given to the influence of concepts such as \(P\)-stability, phase lag and exponential fitting each of which has prompted a large amount of research.
For the entire collection see [Zbl 0835.00026].
For the entire collection see [Zbl 0835.00026].
MSC:
| 65L20 | Stability and convergence of numerical methods for ordinary differential equations |
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
| 65-02 | Research exposition (monographs, survey articles) pertaining to numerical analysis |
| 34A34 | Nonlinear ordinary differential equations and systems |
