𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Runge-Kutta methods for the solution of stiff two-point boundary value problems

✍ Scribed by J.R. Cash

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
847 KB
Volume
22
Category
Article
ISSN
0168-9274

No coin nor oath required. For personal study only.

✦ Synopsis

One of the most popular approaches to the numerical solution of two-point boundary value problems is shooting. However this approach is often ineffective for singularly perturbed problems due to the possible presence of rapidly increasing modes which cannot be dealt with using an initial value solver. In this paper we survey the use of implicit Runge-Kutta methods for such problems. It is shown that certain classes of implicit Runge-Kutta formulae are both stable and accurate for singularly perturbed problems and an efficient implementation of these formulae, based on the use of deferred correction, is described.

πŸ“œ SIMILAR VOLUMES

Explicit Runge-Kutta methods for initial
Explicit Runge-Kutta methods for initial value problems with oscillating solutions
✍ M. Calvo; J.M. Franco; J.I. Montijano; L. RΓ‘ndez πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 888 KB

New pairs of embedded Runge-Kutta methods specially adapted to the numerical solution of first order systems of differential equations which are assumed to possess oscillating solutions are obtained. These pairs have been derived taking into account not only the usual properties of accuracy, stabili