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Equivalent Forms of Multistep Formulas
| Content Provider | Scilit |
|---|---|
| Author | Skeel, Robert D. |
| Copyright Year | 1979 |
| Description | For uniform meshes it is shown that any linear k-step formula can be formulated so that only k values need to be saved between steps. By saving additional m values it is possible to construct local polynomial approximations of degree , which can be used as predictor formulas. Different polynomial bases lead to different equivalent forms of multistep formulas. In particular, local monomial bases yield Nordsieck formulas. An explicit one-to-one correspondence is established between Nordsieck formulas and k-step formulas of order at least k, and a strong equivalence result is proved for all but certain pathological cases. Equivalence is also shown for P(EC) formulas but not for P(EC)E formulas. |
| Related Links | https://www.ams.org/mcom/1979-33-148/S0025-5718-1979-0537967-4/S0025-5718-1979-0537967-4.pdf |
| Ending Page | 1250 |
| Page Count | 22 |
| Starting Page | 1229 |
| ISSN | 00255718 |
| e-ISSN | 10886842 |
| DOI | 10.2307/2006457 |
| Journal | Mathematics of Computation |
| Issue Number | 148 |
| Volume Number | 33 |
| Language | English |
| Publisher | Duke University Press |
| Publisher Date | 1979-10-01 |
| Access Restriction | Open |
| Subject Keyword | Mathematical Physics Text Nordsieck Formulas Equivalent Forms Multistep Formulas K Step |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Algebra and Number Theory Computational Mathematics |
