Where have all the digits gone?
Abstract
We investigate spectral collocation methods for solving differential equations. In particular, we explore the sensitivity of those methods to perturbations or round-off errors. Although the condition numbers of the matrices arising in the computation are often very large, one typically does not observe a comparably large amplification of perturbations. In fact, with zero boundary conditions, there is no amplification.
- Publication:
-
Numerical Analysis and Applied Mathematics ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics
- Pub Date:
- September 2012
- DOI:
- 10.1063/1.4756112
- Bibcode:
- 2012AIPC.1479..258R
- Keywords:
-
- boundary-value problems;
- differential equations;
- 02.30.Hq;
- 02.60.Lj;
- Ordinary differential equations;
- Ordinary and partial differential equations;
- boundary value problems