| Title | Linear multistep methods with constant coefficients and step density control |
| Authors | Gustaf Söderlind, José Diaz López |
| Alternative Location | http://dx.doi.org/10.1016/j..., Restricted Access |
| Publication | Journal of Computational and Applied Mathematics |
| Year | 2006 |
| Volume | 205 |
| Issue | 2 |
| Pages | 891 - 900 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Elsevier Science B.V. |
| Abstract English | In linear multistep methods with variable step size, the method's coefficients are functions of the step size ratios. The coefficients therefore need to be recomputed on every step to retain the method's proper order of convergence. An alternative approach is to use step density control to make the method adaptive. If the step size sequence is smooth, the method can use constant coefficients without losing its order of convergence. The paper introduces this new adaptive technique and demonstrates its feasibility with a few test problems.<br> <br> The technique works in perfect agreement with theory for a given step density function. For practical use, however, the density must be generated with data computed from the numerical solution. We introduce a local error tracking controller, which automatically adapts the density to computed data, and demonstrate in computational experiments that the technique works well at least up to 4th order methods. |
| Keywords | Multistep method variable step size method step size selection step density control nonuniform grid, |
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