Дослідження поведінки наближеного розв’язку нелінійної крайової задачі в околі втрати стійкості
A numerical solution of the nonlinear boundary-value problem is obtained by means of the finiteelements method. Variational relation of a problem of stability analysis in the vicinity of anysolution of the nonlinear problem is formulated. This problem is discretized by means of the sameapproximation...
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| Date: | 2018 |
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| Main Author: | |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України
2018
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| Subjects: | |
| Online Access: | https://www.fmmit.lviv.ua/index.php/fmmit/article/view/60 |
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| Journal Title: | Physico-mathematical modeling and informational technologies |
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Physico-mathematical modeling and informational technologies| Summary: | A numerical solution of the nonlinear boundary-value problem is obtained by means of the finiteelements method. Variational relation of a problem of stability analysis in the vicinity of anysolution of the nonlinear problem is formulated. This problem is discretized by means of the sameapproximations of finite elements methods, as the solution of the nonlinear problem. Theeigenvalue matrix partial problems by a method of iterations in a subspace are reduced to asequence of full matrix problems of small dimension. These problems are transformed to threediagonalones by Householder method and solved by QL-algorithm. The critical value andcorresponding forms of loss of stability in the vicinity of the initial and the final states areanalysed. |
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