| Title | Adaptivity and Computational Complexity in the Numerical Solution of ODEs |
| Authors | Silvana Ilie, Gustaf Söderlind, Robert M. Corless |
| Alternative Location | http://www.sciencedirect.co..., Restricted Access |
| Alternative Location | http://dx.doi.org/10.1016/j..., Restricted Access |
| Publication | Journal of Complexity |
| Year | 2008 |
| Volume | 24 |
| Issue | 3 |
| Pages | 341 - 361 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Academic Press Inc Elsevier Science |
| Abstract English | In this paper we analyze the problem of adaptivity for numerical methods for solving ODEs, both IVPs and BVPs, with a view to generating optimal grids for local error control. The grids are generated by introducing an auxiliary independent variable au and finding a grid deformation map, t=Theta(au), that maps an equidistant grid au_j to a non-equidistant grid in the original independent variable, {t_j}. The optimal deformation Theta is determined by a variational approach. Finally, we investigate the cost of the solution procedure and compare it to the cost of using equidistant grids. We show that if the principal error function is non-constant, an adaptive method is always more efficient than a nonadaptive method. |
| Keywords | Information-based complexity, Adaptive step size control, Adaptive numerical methods, Ordinary differential equations, Initial value problems, Boundary value problems, Hölder mean, |
| ISBN/ISSN/Other | ISSN: 0885-064X |
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