Fifty years of stiffness. (English) Zbl 1216.65083
Simos, Theodore E. (ed.), Recent advances in computational and applied mathematics. Dordrecht: Springer (ISBN 978-90-481-9980-8/hbk; 978-90-481-9981-5/ebook). 1-21 (2011).
Summary: The notion of stiffness, which originated in several applications of different nature, has dominated the activities related to the numerical treatment of differential problems for the last fifty years. Contrary to what usually happens in mathematics, its definition has been, for a long time, not formally precise (actually, there are too many of them). Again, the needs of applications, especially those arising in the construction of robust and general purpose codes, require nowadays a formally precise definition. In this paper, we review the evolution of such a notion and we also provide a precise definition which encompasses all the previous ones.
For the entire collection see [Zbl 1201.65004].
For the entire collection see [Zbl 1201.65004].
MSC:
| 65L04 | Numerical methods for stiff equations |
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
| 34A30 | Linear ordinary differential equations and systems |
| 34B05 | Linear boundary value problems for ordinary differential equations |
| 65L11 | Numerical solution of singularly perturbed problems involving ordinary differential equations |
