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Approximately preserving symmetries in the numerical integration of ordinary differential equations
| Content Provider | Scilit |
|---|---|
| Author | Robert, McL A. C. H. L. A. N. Iserles, Arieh Zanna, Antonella |
| Copyright Year | 1999 |
| Description | We present a general procedure for recursively improving the invariance of a numerical integrator under a symmetry group. If h is a symmetry, we construct the adjoint method $h^{−1}$h. In each time step we apply either the original method or the adjoint method, according to a prescription based on the Thue–Morse sequence. The outcome is a solution sequence which displays progressively smaller symmetry errors, to any desired order in the time-step. The method can also be used to force the solution to stay close to a desired submanifold of phase space, while retaining structural properties of the original method. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/60FD08DBFE0A5CCF5E6F369B57AADA22/S0956792599003927a.pdf/div-class-title-approximately-preserving-symmetries-in-the-numerical-integration-of-ordinary-differential-equations-div.pdf |
| Ending Page | 445 |
| Page Count | 27 |
| Starting Page | 419 |
| ISSN | 09567925 |
| e-ISSN | 14694425 |
| DOI | 10.1017/s0956792599003927 |
| Journal | European Journal of Applied Mathematics |
| Issue Number | 5 |
| Volume Number | 10 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1999-10-01 |
| Access Restriction | Open |
| Subject Keyword | European Journal of Applied Mathematics Ordinary Differential Equation Numerical Integration |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics |
