A unified Krylov-Bogoliubov-Mitropolskii method for solving hyperbolic-type nonlinear partial differential systems
A general asymptotic solution is presented for investigating the transient response of non-linear systems modeled by hyperbolic-type partial differential equations with small nonlinearities. The method covers all the cases when eigen-values of the corresponding unperturbed systems are real, complex...
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| Format: | Article |
| Language: | English |
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Publishing House for Science and Technology
2008-03-01
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| Series: | Vietnam Journal of Mechanics |
| Online Access: | https://vjs.ac.vn/index.php/vjmech/article/view/5607 |
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| author | M. Zahurul Islam M. Shamsul Alam M. Bellal Hossain |
| author_facet | M. Zahurul Islam M. Shamsul Alam M. Bellal Hossain |
| author_sort | M. Zahurul Islam |
| collection | DOAJ |
| description | A general asymptotic solution is presented for investigating the transient response of non-linear systems modeled by hyperbolic-type partial differential equations with small nonlinearities. The method covers all the cases when eigen-values of the corresponding unperturbed systems are real, complex conjugate, or purely imaginary. It is shown that by suitable substitution for the eigen-values in the general result that the solution corresponding to each of the three cases can be obtained. The method is an extension of the unified Krylov-Bogoliubov-Mitropolskii method, which was initially developed for un-darnped, under-clamped and over-clamped cases of the second order ordinary differential equation. The methods also cover a special condition of the over-damped case in which the general solution is useless. |
| format | Article |
| id | doaj-art-becb3e4b8d084f8b9a1a8b58ccb9afb7 |
| institution | DOAJ |
| issn | 0866-7136 2815-5882 |
| language | English |
| publishDate | 2008-03-01 |
| publisher | Publishing House for Science and Technology |
| record_format | Article |
| series | Vietnam Journal of Mechanics |
| spelling | doaj-art-becb3e4b8d084f8b9a1a8b58ccb9afb72025-08-20T02:55:06ZengPublishing House for Science and TechnologyVietnam Journal of Mechanics0866-71362815-58822008-03-0130110.15625/0866-7136/30/1/5607A unified Krylov-Bogoliubov-Mitropolskii method for solving hyperbolic-type nonlinear partial differential systemsM. Zahurul Islam0M. Shamsul Alam1M. Bellal Hossain2Department of Applied Mathematics, Rajshahi University, Rajshahi-6205, BangladeshDepartment of Mathematics, Rajshahi University of Engineering and Technology, Rajshahi-6204, BangladeshDepartment of Mathematics, Rajshahi University of Engineering and Technology, Rajshahi-6204, BangladeshA general asymptotic solution is presented for investigating the transient response of non-linear systems modeled by hyperbolic-type partial differential equations with small nonlinearities. The method covers all the cases when eigen-values of the corresponding unperturbed systems are real, complex conjugate, or purely imaginary. It is shown that by suitable substitution for the eigen-values in the general result that the solution corresponding to each of the three cases can be obtained. The method is an extension of the unified Krylov-Bogoliubov-Mitropolskii method, which was initially developed for un-darnped, under-clamped and over-clamped cases of the second order ordinary differential equation. The methods also cover a special condition of the over-damped case in which the general solution is useless.https://vjs.ac.vn/index.php/vjmech/article/view/5607 |
| spellingShingle | M. Zahurul Islam M. Shamsul Alam M. Bellal Hossain A unified Krylov-Bogoliubov-Mitropolskii method for solving hyperbolic-type nonlinear partial differential systems Vietnam Journal of Mechanics |
| title | A unified Krylov-Bogoliubov-Mitropolskii method for solving hyperbolic-type nonlinear partial differential systems |
| title_full | A unified Krylov-Bogoliubov-Mitropolskii method for solving hyperbolic-type nonlinear partial differential systems |
| title_fullStr | A unified Krylov-Bogoliubov-Mitropolskii method for solving hyperbolic-type nonlinear partial differential systems |
| title_full_unstemmed | A unified Krylov-Bogoliubov-Mitropolskii method for solving hyperbolic-type nonlinear partial differential systems |
| title_short | A unified Krylov-Bogoliubov-Mitropolskii method for solving hyperbolic-type nonlinear partial differential systems |
| title_sort | unified krylov bogoliubov mitropolskii method for solving hyperbolic type nonlinear partial differential systems |
| url | https://vjs.ac.vn/index.php/vjmech/article/view/5607 |
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