Piecewise-linear and bilinear approaches to nonlinear differential equations approximation problem of computational structural mechanics
This paper presents a bilinear approach to nonlinear differential equations system approximation problem. Sometimes the nonlinear differential equations right-hand sides linearization is extremely difficult or even impossible. Then piecewise-linear approximation of nonlinear differential equations c...
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| Format: | Article |
| Language: | English |
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EDP Sciences
2017-01-01
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| Series: | MATEC Web of Conferences |
| Online Access: | https://doi.org/10.1051/matecconf/201711700103 |
| _version_ | 1818412871678164992 |
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| author | Leibov Roman |
| author_facet | Leibov Roman |
| author_sort | Leibov Roman |
| collection | DOAJ |
| description | This paper presents a bilinear approach to nonlinear differential equations system approximation problem. Sometimes the nonlinear differential equations right-hand sides linearization is extremely difficult or even impossible. Then piecewise-linear approximation of nonlinear differential equations can be used. The bilinear differential equations allow to improve piecewise-linear differential equations behavior and reduce errors on the border of different linear differential equations systems areas. The matrices of bilinear differential equations system are estimated through nonlinear programming. The results of proposed approach application are presented. |
| first_indexed | 2024-12-14T10:54:12Z |
| format | Article |
| id | doaj.art-feb2fda1dd6344d8b488e7bf2d350014 |
| institution | Directory Open Access Journal |
| issn | 2261-236X |
| language | English |
| last_indexed | 2024-12-14T10:54:12Z |
| publishDate | 2017-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | MATEC Web of Conferences |
| spelling | doaj.art-feb2fda1dd6344d8b488e7bf2d3500142022-12-21T23:05:03ZengEDP SciencesMATEC Web of Conferences2261-236X2017-01-011170010310.1051/matecconf/201711700103matecconf_rsp2017_00103Piecewise-linear and bilinear approaches to nonlinear differential equations approximation problem of computational structural mechanicsLeibov Roman0Moscow state university of civil engineeringThis paper presents a bilinear approach to nonlinear differential equations system approximation problem. Sometimes the nonlinear differential equations right-hand sides linearization is extremely difficult or even impossible. Then piecewise-linear approximation of nonlinear differential equations can be used. The bilinear differential equations allow to improve piecewise-linear differential equations behavior and reduce errors on the border of different linear differential equations systems areas. The matrices of bilinear differential equations system are estimated through nonlinear programming. The results of proposed approach application are presented.https://doi.org/10.1051/matecconf/201711700103 |
| spellingShingle | Leibov Roman Piecewise-linear and bilinear approaches to nonlinear differential equations approximation problem of computational structural mechanics MATEC Web of Conferences |
| title | Piecewise-linear and bilinear approaches to nonlinear differential equations approximation problem of computational structural mechanics |
| title_full | Piecewise-linear and bilinear approaches to nonlinear differential equations approximation problem of computational structural mechanics |
| title_fullStr | Piecewise-linear and bilinear approaches to nonlinear differential equations approximation problem of computational structural mechanics |
| title_full_unstemmed | Piecewise-linear and bilinear approaches to nonlinear differential equations approximation problem of computational structural mechanics |
| title_short | Piecewise-linear and bilinear approaches to nonlinear differential equations approximation problem of computational structural mechanics |
| title_sort | piecewise linear and bilinear approaches to nonlinear differential equations approximation problem of computational structural mechanics |
| url | https://doi.org/10.1051/matecconf/201711700103 |
| work_keys_str_mv | AT leibovroman piecewiselinearandbilinearapproachestononlineardifferentialequationsapproximationproblemofcomputationalstructuralmechanics |