Backward error analysis for numerical integrators:
Abstract: "We consider backward error analysis of numerical approximations to ordinary differential equations, i.e., the numerical solution is formally interpreted as the exact solution of a modified differential equation. A simple recursive definition of the modified equation is stated. This r...
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| Main Author: | |
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| Format: | Book |
| Language: | German |
| Published: |
Berlin
Konrad-Zuse-Zentrum für Informationstechnik
1996
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| Series: | Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC
1996,21 |
| Subjects: | |
| Summary: | Abstract: "We consider backward error analysis of numerical approximations to ordinary differential equations, i.e., the numerical solution is formally interpreted as the exact solution of a modified differential equation. A simple recursive definition of the modified equation is stated. This recursion is used to give a new proof of the exponentially closeness of the numerical solutions and the solutions to an appropriate truncation of the modified equation. We also discuss qualitative properties of the modified equation and apply these results to the symplectic variable step-size integration of Hamiltonian systems, the conservation of adiabatic invariants, and numerical chaos associated to homoclinic orbits." |
| Item Description: | Literaturverz. S. 27 - 29 |
| Physical Description: | 29 S. graph. Darst. |
Staff View
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| 245 | 1 | 0 | |a Backward error analysis for numerical integrators |c Sebastian Reich |
| 264 | 1 | |a Berlin |b Konrad-Zuse-Zentrum für Informationstechnik |c 1996 | |
| 300 | |a 29 S. |b graph. Darst. | ||
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| 490 | 1 | |a Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC |v 1996,21 | |
| 500 | |a Literaturverz. S. 27 - 29 | ||
| 520 | 3 | |a Abstract: "We consider backward error analysis of numerical approximations to ordinary differential equations, i.e., the numerical solution is formally interpreted as the exact solution of a modified differential equation. A simple recursive definition of the modified equation is stated. This recursion is used to give a new proof of the exponentially closeness of the numerical solutions and the solutions to an appropriate truncation of the modified equation. We also discuss qualitative properties of the modified equation and apply these results to the symplectic variable step-size integration of Hamiltonian systems, the conservation of adiabatic invariants, and numerical chaos associated to homoclinic orbits." | |
| 650 | 4 | |a Differential equations | |
| 650 | 4 | |a Error analysis (Mathematics) | |
| 650 | 4 | |a Recursive functions | |
| 830 | 0 | |a Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC |v 1996,21 |w (DE-604)BV004801715 |9 1996,21 | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-007365851 | |
Record in the Search Index
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| author | Reich, Sebastian |
| author_facet | Reich, Sebastian |
| author_role | aut |
| author_sort | Reich, Sebastian |
| author_variant | s r sr |
| building | Verbundindex |
| bvnumber | BV011002540 |
| classification_rvk | SS 4777 |
| ctrlnum | (OCoLC)37020130 (DE-599)BVBBV011002540 |
| discipline | Informatik |
| format | Book |
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| id | DE-604.BV011002540 |
| illustrated | Illustrated |
| indexdate | 2025-01-10T17:07:56Z |
| institution | BVB |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007365851 |
| oclc_num | 37020130 |
| open_access_boolean | |
| owner | DE-12 DE-703 |
| owner_facet | DE-12 DE-703 |
| physical | 29 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Konrad-Zuse-Zentrum für Informationstechnik |
| record_format | marc |
| series | Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC |
| series2 | Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC |
| spelling | Reich, Sebastian Verfasser aut Backward error analysis for numerical integrators Sebastian Reich Berlin Konrad-Zuse-Zentrum für Informationstechnik 1996 29 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC 1996,21 Literaturverz. S. 27 - 29 Abstract: "We consider backward error analysis of numerical approximations to ordinary differential equations, i.e., the numerical solution is formally interpreted as the exact solution of a modified differential equation. A simple recursive definition of the modified equation is stated. This recursion is used to give a new proof of the exponentially closeness of the numerical solutions and the solutions to an appropriate truncation of the modified equation. We also discuss qualitative properties of the modified equation and apply these results to the symplectic variable step-size integration of Hamiltonian systems, the conservation of adiabatic invariants, and numerical chaos associated to homoclinic orbits." Differential equations Error analysis (Mathematics) Recursive functions Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC 1996,21 (DE-604)BV004801715 1996,21 |
| spellingShingle | Reich, Sebastian Backward error analysis for numerical integrators Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC Differential equations Error analysis (Mathematics) Recursive functions |
| title | Backward error analysis for numerical integrators |
| title_auth | Backward error analysis for numerical integrators |
| title_exact_search | Backward error analysis for numerical integrators |
| title_full | Backward error analysis for numerical integrators Sebastian Reich |
| title_fullStr | Backward error analysis for numerical integrators Sebastian Reich |
| title_full_unstemmed | Backward error analysis for numerical integrators Sebastian Reich |
| title_short | Backward error analysis for numerical integrators |
| title_sort | backward error analysis for numerical integrators |
| topic | Differential equations Error analysis (Mathematics) Recursive functions |
| topic_facet | Differential equations Error analysis (Mathematics) Recursive functions |
| volume_link | (DE-604)BV004801715 |
| work_keys_str_mv | AT reichsebastian backwarderroranalysisfornumericalintegrators |